Post on 03-Oct-2020
Analysis of Freeway Bottlenecks
by
Srinivasa Srivatsav Kandala
A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree
Doctor of Philosophy
Approved June 2014 by the Graduate Supervisory Committee:
Soyoung Ahn, Chair
Ram Pendyala Kamil Kaloush
ARIZONA STATE UNIVERSITY
August 2014
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ABSTRACT
Traffic congestion is a major externality in modern transportation systems with
negative economic, environmental and social impacts. Freeway bottlenecks are one of the
key elements besides the demand for travel by automobiles that determine the extent of
congestion. The primary objective of this research is to provide a better understanding of
factors for variations in bottleneck discharge rates. Specifically this research seeks to (i)
develop a methodology comparable to the rigorous methods to identify bottlenecks and
measure capacity drop and its temporal (day to day) variations in a region, (ii) understand
the variations in discharge rate of a freeway weaving bottleneck with a HOV lane and
(iii) understand the relationship between lane flow distribution and discharge rate on a
weaving bottleneck resulted from a lane drop and a busy off-ramp. In this research, a
methodology has been developed to de-noise raw data using Discrete Wavelet
Transforms (DWT). The de-noised data is then used to precisely identify bottleneck
activation and deactivation times, and measure pre-congestion and congestion flows
using Continuous Wavelet Transforms (CWT). To this end a methodology which could
be used efficiently to identify and analyze freeway bottlenecks in a region in a consistent,
reproducible manner was developed. Using this methodology, 23 bottlenecks have been
identified in the Phoenix metropolitan region, some of which result in long queues and
large delays during rush-hour periods. A study of variations in discharge rate of a
freeway weaving bottleneck with a HOV lane showed that the bottleneck discharge rate
diminished by 3-25% upon queue formations, however, the discharge rate recovered
shortly thereafter upon high-occupancy-vehicle (HOV) lane activation and HOV lane
flow distribution (LFD) has a significant effect on the bottleneck discharge rate: the
ii
higher the HOV LFD, the lower the bottleneck discharge rate. The effect of lane flow
distribution and its relationship with bottleneck discharge rate on a weaving bottleneck
formed by a lane drop and a busy off-ramp was studied. The results showed that the
bottleneck discharge rate and lane flow distribution are linearly related and higher
utilization of the median lane results in higher bottleneck discharge rate.
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Dedicated to my parents
Ratna and Gopala Rao
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ACKNOWLEDGMENTS
First and foremost, I offer my deepest gratitude to my advisor Dr. Soyoung Ahn
for her supervision, advice and guidance. She provided me unflinching encouragement
and support throughout the course of my graduate study and this research work. I would
like to thank Dr. Ram Pendyala and Dr. Kamil Kaloush for serving in my committee.
I am as ever, indebted to my parents, brothers and friends for their love and
support throughout my life. I am also thankful to Tejasri Buddha, Sravani Vadlamani,
Zuduo Zheng, Karthik Konduri, Madhav Garikapati and Priya Gudipudi for their
cheerful company and help in making my graduate study, a memorable experience.
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TABLE OF CONTENTS
Page
LIST OF TABLES ................................................................................................................. vii
LIST OF FIGURES .............................................................................................................. viii
CHAPTER
1 INTRODUCTION ................. .................................................................................... 1
2 LITERATURE REVIEW ............ .............................................................................. 5
Features of Bottleneck Discharge Rate .................................................................. 5
Effectiveness of Hov Lane and Smoothing Effect .............................................. 16
Lane Flow Distribution (LFD) ............................................................................. 18
3 METHODOLOGY .................. ................................................................................ 22
Regional Analysis Methodology .......................................................................... 22
Measurement or estimation of bottleneck discharge rate ....................... 22
Wavelet Transform ............................................................................................... 24
Filtering data noise ................................................................................... 31
Bottleneck activation and discharge rate ................................................. 36
4 REGIONAL BOTTLENECK ANALYSIS ............................................................. 38
Case Study Site and Data ..................................................................................... 39
Identification of Recurrent Bottlenecks ............................................................... 40
Congestion pattern ................................................................................... 41
Sensor coverage of the queue .................................................................. 41
Data……..……………………………………………………………...44
Non-recurrent congestion......................................................................... 45
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CHAPTER Page
Evaluation of Regional Analysis .......................................................................... 47
Regional Bottleneck Analysis .............................................................................. 52
Conclusion ................................................................................................... 56
5 FREEWAY WEAVING BOTTLENECK: BOTTLENECK FEATURES AND THE
SMOOTHING EFFECT OF THE HOV LANE ................................. 59
Site and Data ................................................................................................... 60
Bottleneck Activation and Discharge Rate .......................................................... 63
Variation in Bottleneck Discharge Rate Reduction ........................................... 69
Variations in pre-queue flow ................................................................... 69
Variations in bottleneck discharge rate ................................................... 71
Conclusion ………………………………………………………………77
6 LANE FLOW DISTRIBUTION AND ITS RELATIONSHIP WITH BOTTLENECK
DISCHARGE RATE ............................................................................ 79
Site and Data ................................................................................................... 80
Bottleneck Activations and Congestion Pattern .................................................. 81
Lane flow distribution and its effect on discharge rate ..……………...86
Relationship between discharge rate and LFD during pre-congestion ... 89
Relationship between discharge rate and LFD during congestion ......... 91
Conclusion ................................................................................................... 97
7 CONCLUSION .......................................................................................................... 99
REFERENCES....... ............................................................................................................ 104
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LIST OF TABLES
Table Page
1. Results: Bottleneck Analysis using Wavelet Analysis ......................................... 49
2. Results: Bottleneck Analysis using Regional Analysis ........................................ 50
3. Comparison of Wavelet Analysis and Simpler Analysis ...................................... 51
4. Recurrent Congestion Identified during A.M. Peak Hours (6 - 10 A.M.) ........... 53
5. Recurrent Congestion Identified during P.M. Peak Hours (3 - 7 P.M.) ............... 54
6. Regional Bottleneck Analysis ............................................................................... 58
7. Results: Bottleneck Analysis using Wavelet Analysis ......................................... 66
8. Statistics of Bottleneck Capacity Drop using Wavelet Analysis. ......................... 69
9. Summary Statistics of the Smoothing Effect Magnitude and Duration ............... 74
10. Total Flow-Oscillations Statistics………………………………………………..75
11. A Summary of Regression Result: Bottleneck Discharge Rate vs. Exit LFD and...
HOV LFD…………………………………………...………………………….76
12. Bottleneck Statistics…………..…………………………………………………82
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LIST OF FIGURES
Figure Page
1. Study Section of QEW, Toronto, Canada. (Recreated based on Hall and
Agyemang-Duah (1991)) ................................................................................... .. 6
2. Best-Fit Regression of Unstable-Dense Flows Against Speed. (Courtesy: Polus
and Pollatschek (2002)) ...................................................................................... .. 9
3. Flow-Occupancy Curves with Categorization of Congestion Levels. (Courtesy:
Liu and Wu (2009)) ............................................................................................ 13
4. Illustration of an Active Bottleneck; The Shaded Area Represents a Queue ... 22
5. Illustration of Bottleneck Discharge Rate Measurement ................................... 23
6. Illustration of Most Common Case of Bottleneck Discharge Rate Estimation. 24
7. (a) Fourier Transform of a Continuous Sine Wave Signal (b) Fourier Transform
of a Finite-Length Sine Wave Signal (c) Single-Frequency Spectral Energy Vs.
Time of a Finite-Length Sine Wave Signal Unattainable with Fourier
Transforms ......................................................................................................... . 26
8. Mexican Hat Wavelet Illustration ..................................................................... . 30
9. Wavelet Based the Subband Algorithm ............................................................ . 33
10. (a) De-Noised Speed; (b) De-Noised Flow on 01/08/09, I-10 Eastbound,
Phoenix ............................................................................................................... . 35
11. (a) Times of Queue Onset and Clearance Based on Continuous Wavelet
Transform; (b) Near-Steady State Periods Based on Continuous Wavelet
Transform (06/06/2008) ..................................................................................... . 37
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Figure Page
12. Map of Greater Phoenix Congested Freeway Segments with Coverage of Loop
Detectors and Passive Acoustic Detectors. (Source: Samuelson (2011),
Application: Arcgis 9.3) ..................................................................................... . 40
13. Speed Contour Plot from Matlab of Ideally Located Bottleneck Having Entire
Queue Contained within Detector Coverage Area ........................................... . 42
14. (a)Tail of a Queue not contained within the Detector Coverage Area. (I-10 WB
AM Peak) (b) Head of a Queue Not Contained within the Detector Coverage
Area (Loop 202 WB A.M. Peak) ....................................................................... 43
15. (a)Speed Contour for the Day with Recurrent Congestion on I-10 EB. (P.M.
Peak) (b) Speed Contour for the Day with Non-Recurrent Congestion on I-10
EB. (P.M. Peak) .................................................................................................. 46
16. Schematic of I-10 Eastbound Bottleneck ........................................................... 47
17. Comparison of Wavelet and Regional Analysis ................................................ 51
18. (a) Schematic of the Study Site At I-10 EB, Phoenix, AZ (b) Location of
Recurrent Bottleneck on I-10 EB, Phoenix AZ (c) Typical Speed Contour of
Recurrent Congestion (I-10 EB) ........................................................................ 61
19. (a) Times of Queue Onset and Clearance Based on Continuous Wavelet
Transform; (b) Near-Steady State Periods Based on Continuous Wavelet
Transform (06/06/2008) ..................................................................................... 65
20. Surges in On-Ramp and Off-Ramp Flows Around the Onset Of Queue .......... 68
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Figure Page
21. (a) Pre-Queue Flow vs. Pre-Queue Off-Ramp Flow; (b) Pre-Queue Flow vs.
Pre-Queue On-Ramp Flow. ................................................................................ 71
22. Smoothing Effects Over Time; (a) Temporal Trends of Total Flow vs. Flow in
the HOV Lane; (b) Temporal Trends of Total Flow vs. Flows in the Regular-
Use Lanes and Exit Lanes .................................................................................. 72
23. LFDs vs. Bottleneck Discharge Rate after HOV Lane Activation ................... 77
24. Bottleneck Location on US-101 Southbound (a) Schematic (b) Speed Contour
on 01-31-14 ......................................................................................................... 81
25. Speed Profile of The Upstream Detector on 01/10/2014................................... 83
26. Flow vs. Speed at the Upstream Detector .......................................................... 84
27. LFD vs. Discharge Rate on 01/31/14 at Detector Located Milepost 9.9 .......... 87
28. Cross-Correlation between the Flow and LFD in the Median Lane (01/31/14) 88
29. LFD Vs. Discharge Rate, During Congestion (a) Lane 1 (b) Lane 2 (c) Lane 3
(d) Lane 4 ............................................................................................................ 89
30. LFD Vs. Discharge Rate, During Pre-congestion (a) Lane 1 (b) Lane 2 (c) Lane
3 (d) Lane 4 ......................................................................................................... 91
31. Difference in Magnitudes Between Lane LFDs Vs. Discharge Rate, During
Congestion .......................................................................................................... 93
32. Relationship Between Difference in Flow Between Downstream and Upstream
Detector and Discharge Rate .............................................................................. 95
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CHAPTER 1
INTRODUCTION
Traffic congestion is a major externality in modern transportation systems and has a
negative economic, environmental, and social impact. The 2012 Urban Mobility Report (Schrank
and Lomax, 2012) states that the cost of congestion, in terms of delay and wasted fuel, is
estimated to be about $103 billion in urban areas in the United States. This cost has steadily
increased since 1982, and the trend will likely continue.
One of the key elements that determine the extent of congestion, besides the demand for
travel by automobiles, is freeway bottlenecks. Some studies (e.g. Cassidy and Bertini, 1999)
have shown that the discharge rate of a merge bottleneck can drop by 10 percent upon bottleneck
activation (i.e., onset of queue/congestion). (Note that an “active” bottleneck is characterized by
a queued state upstream and a free-flow state downstream.) In traffic science literature, this
phenomenon is referred to as “capacity drop.” Thus, identifying freeway bottlenecks and
studying the mechanism of their activation and capacity drop are important in improving
operational efficiency and reducing freeway delay. Further, while freeway bottlenecks are
observed to exhibit reproducible features, they still display temporal variations. For example, the
reduction in bottleneck capacity upon activation is observed to vary (e.g. as low as 1.5 percent).
Whether these variations are merely stochastic fluctuations (and therefore statistically
insignificant) or occur due to the changes in traffic features (e.g. on-ramp inflow, lane-changing
rates) is an open question yet to be explored in detail.
In recent years, there have been efforts to understand the characteristics of freeway
bottlenecks. Many studies have shown that the features related to bottleneck activations exhibit
regularities and are often reproducible. For example, researchers have observed over multiple
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days that the reduction in bottleneck discharge rate is attributable to systematic lane-change
maneuvers from the rightmost lane (shoulder lane) upstream of the merge to faster lanes to the
left (Cassidy and Rudjanakanoknad, 2005). Moreover, the resulting queues propagate in ways
predictable by a simple kinematic wave theory (Newell, 1993). For example, the wave marking
the onset of a queue propagates backward in space at the speed of approximately 10 mph as
predicted by the kinematic wave theory, and numerous studies (e.g. Smilowitz and Daganzo,
2000) reported similar findings. However, freeway bottlenecks still present many puzzling
aspects including variation of capacity reduction and influencing factors.
There have not been many efforts in the past to systematically identify bottlenecks and
measure the capacity drop on a regional network. This could be done by developing a
methodology comparable to the rigorous methods to provide a better understanding of detailed
features of freeway bottlenecks in a region and their temporal (day-to-day) variations.
Developing effective countermeasures to improve freeway operations would benefit from more
detailed analysis of various bottleneck features, particularly the capacity drop. Prioritizing the
bottlenecks by ranking them based on the capacity drop would help the local governing body to
focus on the bottlenecks that require immediate attention.
The primary objective of this research is to provide a better understanding of factors for
variations in bottleneck discharge rates. Specific objectives are:
Regional Bottleneck Analysis: The objective here is to develop a methodology which could
be used efficiently to identify and analyze freeway bottlenecks in a region in a consistent,
reproducible manner. To this end, a simple analysis methodology was developed for a regional
analysis and compared to a more rigorous method based on a spectral analysis technique. The
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comparative analysis was conducted for the Phoenix metropolitan region to gauge the trade-off
between precision and efficiency.
Using the regional analysis methodology, 23 bottlenecks have been identified, some of which
result in long queues and large delays during rush-hour periods. For these bottlenecks, a number
of performance measures were obtained, such as the duration of congestion, length of the
congestion, vehicle miles traveled (VMT), vehicles hours traveled (VHT), and bottleneck
discharge rate (where it can be measured or estimated). The identified bottlenecks were ranked
according to the capacity drop in terms of flow and percent reduction in flow.
Bottleneck Features and The Smoothing Effect of the HOV lane on a Freeway Weaving
Bottleneck: The objective here is to study the variations in discharge rate of a freeway weaving
bottleneck. Data obtained near a freeway weave bottleneck show that the bottleneck discharge
rate diminished by 3-25% upon queue formations. The discharge rate, however, recovered
shortly thereafter upon high-occupancy-vehicle (HOV) lane activation. A statistical analysis
showed that HOV lane flow distribution (LFD) has a significant effect on the bottleneck
discharge rate: the higher the HOV LFD, the lower the bottleneck discharge rate. This finding
supports the existence of “smoothing effect” which has been shown to arise at a merge
bottleneck due to fewer disruptive lane changes with activation of HOV lane.
The Effect of Lane Flow Distribution (LFD) on the Reduction of Bottleneck Discharge Rate:
Cassidy et.al (Cassidy and Bertini, 1999) observed that before the bottleneck activation high
flows were created as a result of vehicle lane changing towards the median lane. They observed a
decrease in discharge rate in all the lanes after the bottleneck activation. This research focusses
on examining the relationship between lane flow distributions and bottleneck discharge rate
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(variation and magnitude). The work is ongoing using the data obtained from a bottleneck on
US-101 southbound in Los Angeles County in California.
Note that a spectral analysis method is used for II and III using high-resolution 20-second
and 30-second data. Noise in the data is a major problem especially when dealing with high
resolution data. In this research, a methodology has been developed to de-noise raw data using
Discrete Wavelet Transforms (DWT). The de-noised data is then used to precisely identify
bottleneck activation and deactivation times, and measure pre-congestion and congestion flows
using Continuous Wavelet Transforms (CWT).
The rest of the document is organized as follows. Chapter 2 describes the literature review,
Chapter 3 discusses the methodology that has been used in this research, and Chapter 4 presents
the regional analysis of bottlenecks in Phoenix metropolitan region. Chapter 5 presents empirical
analysis of bottleneck features at a freeway weaving bottleneck using a spectral analysis
technique, called wavelet transform. Chapter 6 will provide analysis of the relationship between
lane flow distribution (LFD) and bottleneck discharge rate.
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CHAPTER 2
LITERATURE REVIEW
Chapter 2 describes the review of literature in three areas: (i) the features of bottleneck
discharge rate, (ii) effectiveness of HOV lane (including the smoothing effect), and (iii) lane
flow distribution. A number of prominent papers on bottlenecks and their related features are
reviewed and described below.
Features of bottleneck discharge rate
This section summarizes several key empirical studies that analyzed traffic features
around freeway bottlenecks.
Empirical evidence of capacity drop
Hall et al. (Hall and Agyemang-Duah, 1991) studied the bottleneck capacity drop
phenomenon using 30-second data collected from a segment on Queen Elizabeth Way, Toronto,
Canada (see Figure 1) in 1990. An active bottleneck typically occurred between stations 22 and
23 in the figure near the Cawthra Rd. interchange. The times of queue onsets and dissipations
and the transition periods (i.e., the periods during which high pre-queue flows were observed
momentarily, followed by marked drops in flow) were measured using the loop detector data
obtained downstream of the active bottleneck (station 25). These times were confirmed by a t-
test, e.g., the differences in flow during transition and after were statistically different. Hall and
Agyemang-Duah computed the mean pre-queue and queue discharge flows by averaging the
flow rates before and after the start of the queue, respectively, at station 25. They found based on
the t-test that the difference between them was significant for 16 of 20 days at 5 percent
significance level. The pre-queue flow rates were larger than the queue discharge rates by about
6
5-6 percent, indicating a capacity drop at the onset of the queues. Finally, they found that the
distribution of queue discharge flows were Gaussian-distributed.
Figure 1. Study section of QEW, Toronto, Canada. (Recreated based on Hall and Agyemang-Duah (1991))
Cassidy et al. (Cassidy and Bertini, 1999) analyzed bottleneck discharge rates at two
freeway bottleneck locations, Queen Elizabeth Way (QEW) and Gardiner Expressway near
Toronto, Canada using high-resolution 30-second (QEW) and 20-second (Gardiner Expressway)
loop detector data for three days. Oblique N-curves (cumulative vehicle counts vs. time on an
oblique time axis) were constructed for each detector station to better reveal changes in traffic
flow/state. Furthermore, the vertical displacements between two N-curves (after correcting for
inflows and outflows) at neighboring detector stations represented vehicle accumulations
between the stations. Similarly oblique T-curves (cumulative occupancy vs. time on an oblique
time axis) were constructed to reveal changes in traffic occupancy/density. Based on these
cumulative N- and T-curves, the active bottleneck locations and the start and end times of queues
were identified systematically; for instance, the start of queue was accompanied by a sharp
increase in occupancy and a reduction in flow. A capacity drop of nearly 8 percent was observed
on QEW, while it varied from 4 percent to 10 percent on Gardiner Express. They observed that
the bottlenecks occurred at the same locations and the discharge rates upon bottleneck activation
were nearly constant over time.
Cawthra Rd. Dixie Rd.
Station 21 Station 22 Station 23 Station 24 Station 25 Station 26
Active Bottleneck
7
Bertini et al. (Bertini and Leal, 2005) studied the traffic features at a freeway lane drop at
two sites, M4 motorway (U.K.) and I-494 (Minneapolis, USA). They used oblique curves of
cumulative vehicle count, time-mean speed, and occupancy vs. time to analyze bottleneck
discharge rate. Upon bottleneck activation, they observed reductions in bottleneck discharge rate
of nearly 10 percent, accompanied by propagations of shock waves at 3-4 mph. They also
observed that oscillations (stop and go traffic) traveled upstream of the bottleneck at nearly
constant speeds independent of the location within the queue. No oscillations were observed
downstream of the bottleneck.
There are other studies (Elefteriadou et al., 1995; Chung and Cassidy, 2004; Cassidy and
Rudjanakanoknad, 2005; Laval et al., 2005; Chung et al., 2007; Yeon et al., 2007; Lee and
Cassidy, 2009; Rudjanakanoknad and Akaravorakulchai, 2011) that have reported evidence of
capacity drop. These studies were described later in the chapter.
Traffic models that capture capacity drop
It is well documented that the seminal Kinematic Wave model (Lighthill and Whitham,
1955; Richards, 1956; Newell, 1993a; 1993b; 1993c) is unable to reproduce the capacity drop
phenomenon (see Nagel and Nelson, (2005) for example). Earlier remedies included defining
reverse-lambda shaped fundamental diagrams, thereby inducing capacity drop exogenously (e.g.,
Koshi et al., 1983; Hall and Hall, 1990). Laval and Daganzo (2006) sought to describe the
physical mechanism by developing a hybrid model that incorporates lane-changing, bounded
vehicle acceleration and heterogeneous vehicle characteristics in a macroscopic framework.
They conjectured that lane-changes by merging vehicles create voids in traffic streams due to
bounded accelerations and that the voids persist and propagate downstream with the traffic,
8
resulting in a reduction in bottleneck discharge flow. Leclercq et al. (2011) further developed a
merge model that endogenously incorporate capacity drop.
Elefteriadou et al. (Elefteriadou, Roess and McShane, 1995) studied the stochastic nature
of breakdowns at freeway merge junctions using the database from NCHRP Project 3-37,
Capacity of Ramp-Freeway Junctions. At three sites, one in Chicago, Illinois and two in
Orlando, Florida, they observed that the breakdowns occurred at these sites at relatively lower
flows compared to maximum observed flows, indicating that breakdowns need not occur only at
capacity flows, thereby contradicting the Highway Capacity Manual. Using videos at the sites,
they observed breakdowns whenever there were clusters of vehicles approaching the freeway
through the on-ramps. In their study, clusters were defined as groups of three or more vehicles
with headways not exceeding 3 seconds or spacing of 54 m (0.033 miles) traveling at a speed
approximately equal to 64 km/h (~40 mph). They concluded that occurrence of breakdowns at
freeways is a probabilistic process and formulated a probabilistic model of breakdown
occurrence as a function of the occurrence of vehicle clusters on the on-ramp and vehicles on the
right-most lane (shoulder lane). However, the model was not fully validated due to limited data
availability. They further observed that the probability of breakdown occurrence increases with
respect to on-ramp flow up to 1,500 vehicles per hour (vph) but does not change much beyond
1,500 vph.
Polus et al. (Polus and Pollatschek, 2002) defined momentary capacity as the intersection
of best-fit regression lines of unstable (congested) and dense (near-capacity) flows against speed
as shown in Figure 2. They found that the momentary capacity was stochastic in nature. They
used 5-minute loop data for speed and flow for three days from three busy urban freeway
facilities in Tel Aviv. Based on the 5-minute data, they obtained regression lines and the
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corresponding estimated parameters for unstable and dense flows and determined a momentary
capacity. Using Monte Carlo simulations, they estimated the distribution of the capacity based on
the properties of the estimated regression parameters (i.e. the expected values and the standard
errors), after which they generated 1,000 random regression lines for unstable and dense flows
and estimated the momentary capacity for each simulation run. The simulation result showed that
the momentary capacity is gamma-distributed.
Figure 2. Best-fit regression of unstable-dense flows against speed. (Courtesy: Polus and Pollatschek (2002))
Brilon et al. (Brilon, Geistefeld and Regler, 2005) defined capacity as “the traffic volume
below which traffic still flows and above which the flow breaks down into stop-and-go or even
standing traffic.” They analyzed data from 15 freeway sections near Cologne, Germany. Using
the Product Limit method, they found that capacity, which is stochastic in nature, follows a
Weibull distribution with a nearly constant shape parameter. (The Product Limit method is
normally used for lifetime data analysis where death is termed as a failure event. In Brilon et al.,
traffic breakdown is termed as a failure event.) They defined three different traffic states: fluent,
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synchronized, and congested. They concluded that transitions between traffic states occur
spontaneously in the order of fluent traffic, breakdown, synchronized state (transition state), and
then congested state. They further observed that the flow after traffic recovery to the fluent state
was less than the flow prior to the breakdown, representing traffic hysteresis. An average
capacity drop of 1,180 vph was observed across the 15 freeway sections analyzed, but the values
varied widely from site to site. The risk of breakdown was particularly high when the freeway
was saturated over 90 percent of its estimated capacity. They also found that capacity was
reduced by 11 percent on a wet surface and that darkness (light conditions) did not affect the
capacity distributions. They also concluded that a controlled-access freeway section has a higher
capacity (by 3 percent) than a highway with intersections.
Yeon et al. (Yeon, Henrandez and Elefteriadou, 2007) defined four different types of
capacity flows: maximum pre-breakdown flow (maximum flow within 2 hours before the
breakdown), breakdown flow (5-minute flow per lane just before the breakdown), maximum
queue discharge flow (maximum flow during congestion), and average queue discharge flow
(average flow during the congestion). They measured these flows on different freeway segments
along US-202 southbound near Philadelphia, PA. In their study, they observed that diverging
segments have larger capacity flows than merging segments on average. Based on the analysis of
variance (ANOVA), they reported that these capacity flows are statistically different across time
of day, though they did not change much across day of the week. Of the different types of
capacity flows, the maximum pre-breakdown flow was found to be the largest, while the average
queue discharge flow was the smallest.
Factors influencing capacity drop
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Cassidy et al. (Cassidy and Mauch, 2001) examined the relationship between flow and
density on queued freeway segments using 20-second loop data during two morning periods on
QEW. This site experienced higher on-ramp flows than off-ramp flows, which resulted in
improvement in queued vehicular speeds toward the bottleneck. They used oblique N- and T-
curves to verify bottleneck capacity drops and examine the features of queues upstream. Notably,
they found that there is a well-defined relationship between flow and vehicle accumulation (thus
density) on a homogenous freeway segment. Moreover, the simple hydrodynamic theory of
Newell (1993) is adequate to predict the propagation of a freeway queue.
Cassidy et al. (Cassidy and Rudjanakanokand, 2005) have studied the effect of on-ramp
metering at an isolated merge bottleneck. They observed that the queue initially formed in the
shoulder lane and spread to the left lanes as slow vehicles maneuvered toward the left lanes.
They found that by metering the on-ramp, the shoulder lane accumulation reduced and higher
bottleneck discharge flows were attained. However, they cautioned that the on-ramp metering
schemes should be adopted based on freeway conditions, such as vehicle accumulations near the
on-ramp, to gain significant increase in the capacities.
Ogut et al. (Ogut and Banks, 2005) studied the nature of transitions from uncongested to
congested flow using 30-second vehicle counts and occupancy data from five freeway sections in
San Diego. They defined speed drop as an event that satisfies the following conditions: a speed
reduction of 10km/hr (6.2 mph) or larger that lasts for at least 15 minutes, or a speed reduction
that propagates upstream as a shock wave, accompanied by reductions in flow at upstream
locations. They analyzed the spatial sequences of speed drops at each site and identified three
patterns. Type A, which is the most typical pattern, is characterized by a speed drop occurring at
the most downstream detector of the study section and then moving upstream. Type B is
12
characterized by two or more bottlenecks with a upstream bottleneck activating first. Type C
displays more complex patterns. There, authors observed that some of speed sequences were out
of order; for example, speed drops occurred at the upstream-most detector first and then at
another detector in the middle. These patterns indicated the presence of more than one
bottleneck. They computed the percentage of breakdowns corresponding to these types of speed
drops at each site. Among the five study sites, the observed speed drops corresponded mostly to
types A and B, with an exception of one site, where complex patterns (type C) were observed. To
verify if variations in demand or a variation in capacity caused these patterns, a sample of speed
drops observed during 15 days was further analyzed. Oblique cumulative plots were examined
for increases in flow prior to the breakdowns, and the results showed that these variations in
breakdowns were due to variations in capacity rather than variations in demand.
Chung et al. (Chung, Rudjanakanoknad and Cassidy, 2007) obtained a correlation
between density and capacity drop on three bottlenecks: a merge bottleneck on I-805 near San
Diego, CA, a reduced-lane bottleneck on SR 24 near San Francisco, CA, and a horizontal-curve
bottleneck on Gardiner expressway in Toronto, Canada. A reduction in bottleneck discharge flow
occurred shortly after the density increased beyond a certain threshold level. For the three
bottlenecks in the study, the capacity drops ranged from 3 percent to 18 percent. The authors
further concluded that capacity drops can be avoided by implementing traffic control schemes
that regulate density.
Liu et al. (Liu and Wu, 2009) considered the influence of downstream traffic in defining
freeway operational capacity. They noted that freeway capacity depends on the prevailing traffic
conditions and is not a single value. They studied the stochasticity of freeway capacity using
loop detector data at three stations along Trunk Highway 169 northbound in the Twin Cities area.
13
They defined freeway operational capacity as “the maximum hourly rate at which vehicles
reasonably can be expected to traverse a point or uniform section of a lane or roadway during a
given time period under prevailing traffic conditions.” They used a flow-density (FD) method,
which is based on the flow-density or flow-occupancy curves, to determine the operational
capacity. The maximum flow rates under different congestion levels (categorized by occupancy
in increments of 5 percent as shown in Figure 3) on multiple days were used to determine the
probabilistic distribution of operational capacities. It was found that, within each congestion
level, the operational capacities are normally distributed. Further, a sensitivity analysis revealed
that the categorization of the congestion level affects the operational capacity. They further
plotted the mean operational capacities at different congestion levels, which showed the same
general trend that an increase in occupancy results in lower operational capacity. The authors
defined a probabilistic function for capacity as a function of occupancy to determine the risk
level (defined as the probability of traffic breakdown) of freeway capacity.
Figure3. Flow-occupancy curves with categorization of congestion levels. (Courtesy: Liu and Wu (2009))
Zhang et al. (Zhang and Levinson, 2009) studied the effectiveness of ramp metering in
the Twin Cities in mitigating the impact of 27 bottlenecks. They analyzed data collected from
nearly 4,000 single-loop detectors for seven weeks without ramp metering and another seven
14
weeks with ramp metering in 2000. To identify active bottlenecks, they defined three traffic
regimes based on traffic density: a congested regime if the density is larger than 39 vehs/km/lane
(24.23 vehs/mile/lane), a free-flow regime if the density is smaller than 31 vehs/km/lane (19.26
vehs/mile/lane), and a transition regime if the density is in between. The threshold values for the
density were determined from visual inspection of the time-series occupancies and cumulative
count curves obtained from more than 30 breakdowns on Trunk Highway 169 and I-94. They
formulated a number of hypotheses to determine the impact of ramp metering on capacity (e.g.,
if pre-queue transitions, defined as the period in which the flow is higher than the queue
discharge flow prior to the breakdown, exist, if pre-queue or queue discharge flows are higher
with metering, if ramp metering can prolong the pre-queue transition period) and concluded that
overall, ramp metering can increase the bottleneck capacity.
Patire et al. (Patire and Cassidy, 2011) studied the congestion mechanism of a three lane
uphill expressway segment, with no ramps, in Japan. They analyzed 14 days of loop detector
data and observed persistent congestion in all the three lanes in the upstream detector and free
flow conditions at the immediately downstream detector. They observed a long run output flow
drop (capacity drop) ranging from 4-11 percent during the study period. They found an increase
in the shoulder lane flow (increased utilization) during the congestion period. They observed low
shoulder lane flows in the initial duration of congestion. Due to the high demand and speed
disturbances induced on the median and central lanes, the vehicles migrated to the shoulder lane
during this period. They observed that once the flow on the shoulder lane increased due to the
increase in the demand the lane changes became more disruptive resulting in the capacity drop.
Studies on weaving bottlenecks
15
Most existing studies in the literature analyzed bottlenecks around merge or diverge
sections, and studies on weaving bottlenecks are relatively rare. Some notable exceptions are Lee
et al. (Lee and Cassidy, 2009) and Rudjanakanoknad et al. (Rudjanakanoknad and
Akaravorakulchai, 2011). Lee et al. (Lee and Cassidy, 2009) studied the mechanism of
bottleneck activations on two freeway weaving sections in California that each formed due to a
busy on-ramp and a busy off-ramp immediately downstream. Each of these sections has an
auxiliary lane connecting the on-ramp and the off-ramp. They found that the bottleneck became
active when freeway-to-ramp (F-R) maneuvers occurred near the on-ramp and that the bottleneck
discharge rate varied by the rate of F-R maneuvers. Moreover, lower on-ramp flows induced
greater F-R maneuvers near the on-ramp and resulted in lower discharge rates. In contrast, higher
on-ramp flows induced F-R maneuvers away from the on-ramp and resulted in higher discharge
flows. Based on the empirical findings, they formulated a mandatory lane changing model in
which the lane changing decision is a function of the distance to the weaving section’s diverge
area, number of lanes to be crossed to reach the target lane and the difference in densities in the
current and the target lanes.
Rudjanakanoknad et al. (Rudjanakanoknad and Akaravorakulchai, 2011) studied a weave
bottleneck in central Bangkok that formed due to busy on-ramp and off-ramp. They analyzed
video data collected during morning peak hours on two days. They observed that the capacity of
the weaving bottleneck varied over time, and the variations were correlated with the upstream
freeway flow, on-ramp and off-ramp flows. Specifically, lane changes from slow to fast lanes
due to a surge in on-ramp flow resulted in an increase in bottleneck discharge rate, whereas lane
changes from fast to slow lanes due to an increase in off-ramp flow resulted in reduction of
bottleneck discharge rate. Based on their findings, they formulated a basic structure to model the
16
capacity of a weaving bottleneck in terms of several factors: lane-wise flows, on-ramp and off-
ramp flows, and number of lane changing maneuvers (fast to slow lanes or slow to fast lanes.
It is evident from the literature review that traffic breakdown is probabilistic, highly site-
specific, and not always reproducible. It has also been found that the capacity drop varies by time
and site and that many factors may be responsible for its variations.
Effectiveness of HOV lane and smoothing effect
This section summarizes several key studies that focusses on the effectiveness of HOV
lanes and smoothing effect and their influence on the traffic flow conditions.
Dahlgren (Dahlgren, 1998; 2002) studied the effectiveness of implementation of HOV vs.
HOT lanes on freeways. The author concluded that if the delay is relatively low (< 35 minutes)
and a proportion of HOVs is less than 20 percent, adding a general purpose lane to the existing
freeway is more effective than adding either an HOV or HOT lane. If the initial delay is high and
accompanied by a high proportion of HOVs (mu ch larger than 20 percent) then adding an HOV
lane is more effective. If the delay is high but the proportion of HOVs is close to 20 percent, an
HOT lane serves as a better alternative to an HOV lane.
Chen et al. (Chen, Varaiya and Kwon, 2005) evaluated HOV lane effectiveness on a
freeway in the San Francisco Bay area and concluded that the HOV lane would increase the
overall congestion on the freeway. They observed that the activation of HOV lane decreases the
capacity of the non-HOV lanes, thereby affecting the overall capacity in a negative way. They
termed this phenomenon as “HOV congestion penalty”. They also observed reductions in speed
and flow in the HOV lane in spite of being in the free flow regime. They termed this as “HOV
capacity penalty”. They explained that the low speed in the HOV lane could be a result of HOV
17
vehicles entering the HOV lane from slow, non-HOV lanes and reduction in speed due to risk
perception induced by the large speed difference between the HOV and non-HOV lanes.
Kwon et al. (Kwon and Varaiya, 2008) have further computed the “HOV capacity
penalty” to be 20 percent. They suggested that the HOV lane actuation increases the demand on
the non-HOV lanes and thus increases the net delay. They also concluded that the HOV lane
actuation does not increase the person throughput significantly and is also insensitive to travel
time saving in both long term and short term.
On the contrary, Menendez et al. (Menendez and Daganzo, 2007) showed using
simulations that the presence of an HOV lane diminishes the disruptive lane changes (smoothing
effect) and therefore can increase the capacity of the general purpose lanes. They studied the
effect of HOV lanes in three different scenarios, one without bottlenecks, one with a diverge
bottleneck and one with a merge bottleneck. They observed increases in capacity in the general
purpose lanes at isolated bottlenecks and decreases in capacity of the general purpose lanes only
at some idealized locations (freeway sections without bottleneck). They also concluded that if
properly deployed, HOV lanes can reduce the person-hours of delay in the system.
Cassidy et al. (Cassidy, Jang and Daganzo, 2010) found that the smoothing effect in fact
exists and is reproducible at different sites and on different days. It was observed that the
smoothing effect is the largest in the lane immediately adjacent to the HOV lane and decreases as
away from the HOV lane. The smoothing effect is the least or negligible in the shoulder lane.
They observed an increase in bottleneck discharge flow as high as 21 percent due to the
smoothing effect. They observed a reduction in both person delay and vehicle delay due to the
smoothing effect.
18
In summary, the studies cited above suggest that lane-changes, induced by merging and
diverging flows, diminish the bottleneck discharge rate and that the activation of a HOV lane can
remedy this impact by discouraging disruptive lane-changes. These previous studies primarily
analyzed the smoothing effect on merge and curve bottlenecks. The present study corroborates
the existence of smoothing effect on a weave bottleneck. Moreover, this study examines the
smoothing effect in more depth by analyzing its temporal trends and influencing factors in a
statistically rigorous manner. We analyzed data from 33 days using a spectral analysis tool called
wavelet transform to systematically de-noise the raw data, unveil underlying trends, and identify
times of queue onset and steady-state periods.
Lane flow distribution (LFD)
This section summarizes several key studies on lane flow distribution.
Carter et.al (Carter, Rakha and Van Aerda, 1999) studied the lane to lane variations in
flow and speed on data from 30 days at 27 detector locations on Queen Elizabeth Way, Canada.
They observed that the interaction between speed and flow on different lanes is significantly
different. The study used analysis of variance (ANOVA) approach to find out if the lane to lane
variations in speed and flow are significantly different. Using ANOV approach they also studied
the interaction between speed and flow across different lanes. They also concluded that the
capacity parameters varied significantly across different sites and day of the week has a
relatively less effect on the variability of flow and speed in different lanes.
Cassidy et.al (Cassidy and Bertini, 1999) studied the bottleneck features upstream and
downstream of a bottleneck located on Gardiner expressway in Toronto, Canada. They observed
that before the bottleneck activation, high flows were created as a result of vehicle lane changing
19
towards the median lane. They observed a decrease discharge rate in all the lanes after the
bottleneck activation.
Amin et al. (Amin and Banks, 2005) have studied the effects of freeway and ramp flows
on the lane flow distribution on five freeway segments in the San Diego, California. They looked
at how the relationships between freeway/ramp volumes and lane flow distributions varied by
time and location. They found that the lane flow distribution of the lanes is significant effected
by the freeway flow and not by the on-ramp flow. They concluded that there was a significant
variation in the lane flow distributions of the lanes by time of day. They noticed that these
variations by time of the day are consistent at different locations in the same freeway segment
however, they differed for different segments. They found that the lane flow distribution in the
median lane increases with an increase in freeway volume.
Hong et al. (Hong and Oguchi, 2007) have studied the lane flow distributions and speed-
flow relationships under unsaturated flow conditions on roadways in Japan. They studied the
lane-use patterns by different vehicles and speed-flow relationships in different lanes for
different roadways sections on multi-lane motorways in Japan. They concluded that the
passenger cars and heavy vehicles showed significant difference in their lane use patterns. They
also found that rainfall has a significant effect on the speed-flow relationship and heavy vehicle
proportion on the motorway. They developed models to estimate the average patterns of lane use
and speed-flow relationships on a lane given the proportion of vehicle type on each lane not
considering the roadway geometric conditions.
Lee et.al. (Lee and Park, 2010) have studied the lane flow distributions on a 2, 3 and 4
lane freeway segments during different traffic conditions. They used density measure instead of
flow to represent lane flow distributions. They found that during uncongested traffic regime, lane
20
flow ratio of median lane increased continuously and the magnitude of the lane flow distribution
across all lanes was nearly the same as the congestion level increased. They also observed an
increase in lane flow ratio in the median lane during the transition regime and lane flow ratio in
middle and right most lanes decreased with increase in density. They also concluded that the lane
flow ratio is effected by the truck volume on the freeway segments.
Knoop et al. (Knoop et al., 2010) studied the effect of variable speed limits on lane flow
distribution near merging zones on A12 motorway eastbound in Netherlands. They observed that
the right-most lane is underutilized on the motorway near a merging zone. They found that a
variable speed limit of 60 km/h has a significant effect on the lane flow distribution and during
this variable speed limit, the flow on the right increased thereby increasing the road capacity.
However, they noticed that at the speed limit of 60km/h the merging process from the on-ramp to
the motorway became more difficult which increased the congestion on the on-ramp. They
concluded that variable speed limits near an on-ramp have significant effect on the lane flow
distribution and should be considered when implementing variable speed limits on a motorway.
Duret et al., (Duret, Ahn and Buisson, 2012) studied the lane flow distribution in free-
flow regime on a three-lane freeway in France. Their study was based on the data collected from
the site located on A7/E15 south Lyon, France. They found that in free-flow regime, the
proportion of flow in the median flow is directly proportional to the total flow. They observed a
reverse trend in the center and shoulder lanes. They found that the relationship between lane flow
distribution and the total is linear. They observed significant under-utilization of the shoulder
lane, which could contribute to lower flow at the onset of congestion. They found that the under-
utilization of the shoulder lane can be in part mitigated by banning trucks and/or implementing
VSLs, both of which had a speed harmonization effect across lanes.
21
In summary, the studies explored the relationship of speed and flow across different lanes
with the total flow on the freeway segments. They observed that high flows before the bottleneck
activation were associated with vehicle lane changes towards the median lane and observed
reduction in flows in all the lanes after the bottleneck activation. However, not much work has
been done on studying the relationship of lane flow distributions at bottleneck locations and their
effect on the reduction/variation in bottleneck discharge rate. This research focuses on examining
the relationship between lane flow distribution and its effect on bottleneck discharge rate at a
bottleneck location on US-101 southbound in Los Angeles County in California.
22
CHAPTER 3
METHODOLOGY
This Chapter describes the methodology of the current research used in the regional
bottleneck study and a rigorous methodology based on a spectral technique called wavelet
transform.
Regional analysis methodology
This section describes the regional methodology procedures for identifying major
recurrent freeway bottlenecks and measuring or estimating the reductions in their discharge rates
(i.e., capacity drop). Specifically, the section provides the definition of an “active bottleneck”
and the methods to measure or estimate bottleneck discharge rates.
Measurement or estimation of bottleneck discharge rate. A bottleneck is “active” if
traffic downstream of the bottleneck is freely flowing and traffic upstream is congested, as
illustrated in Figure 4. In this study, speed below 45 mph is classified as “congestion” in using
the 5-minute data. Thus, an active bottleneck is located by identifying a pair of neighboring
detector stations with the upstream detectors exhibiting congested speed and the downstream
detectors exhibiting free-flow speed (> 45 mph). We analyzed all recurrent active bottlenecks
that persisted over 30 minutes or longer.
Figure4. Illustration of an active bottleneck; the shaded area represents a queue.
Active bottleneck
Queue
23
To analyze the reduction in bottleneck discharge rate (i.e., capacity drop), the maximum
flow prior to a bottleneck activation and the discharge rate during congestion are measured.
More specifically, the pre-congestion flow is the maximum flow prior to the bottleneck
activation, and the bottleneck discharge rate during congestion is measured as the average flow
during congestion. Then the capacity drop is measured as the difference between these two
flows. The details of how these flows are measured are discussed later.
Ideally, bottleneck discharge rates should be measured at a location immediately
downstream of a bottleneck with flows conserved throughout. This is illustrated in Figure 5. In
this hypothetical example, a merge bottleneck is located between stations 1 and 2; thus,
bottleneck discharge rates can be measured directly at station 2 since flow is conserved between
the bottleneck and station 2.
Figure5. Illustration of bottleneck discharge rate measurement.
For other types of recurrent bottlenecks, discharge rates are estimated rather than directly
measured. For instance, Figure 6 shows a typical detector configuration around a merge
bottleneck. Detectors (at station 1) are placed on the mainline and the on-ramp immediately
upstream of the hypothetical merge; and an off-ramp is located between the bottleneck and the
downstream detector station (station 2 in the figure). In cases like this, the bottleneck discharge
Active bottleneck
Queue
Station 1 Station 2
24
rate cannot be measured at station 2 since flow is not conserved due to diverging flow; i.e., the
flow at station 2 represents the bottleneck discharge rate minus the diverging flow. Instead, the
bottleneck discharge rate is estimated by summing the mainline and the on-ramp flows at station
1. Alternatively, the off-ramp flow can be added to the flow at station 2; however, off-ramp
counts were not available at most locations.
Figure6. Illustration of most common case of bottleneck discharge rate estimation. Finally, bottleneck discharge rates cannot be measured or estimated on several freeways
because on-ramp counts were not available or bottlenecks were not contained within the detector
coverage area. For these cases, we report flows (rather than bottleneck discharge rates) before,
during, and after congestion at the stations nearest to the bottlenecks.
Wavelet transform
In this research, the wavelet transform (WT) is used to de-noise the raw data, precisely
identify bottleneck activation and deactivation times, and measure pre-congestion and congestion
flows. These events are typically marked by sharp changes in speed and/or flow, which can be
detected effectively by WT. In this chapter, we provide detailed background information of WT.
In the presence of noise, it is often not feasible to obtain critical information precisely
from the raw signal (e.g., 20-second detector speed or flow data). Mathematical transformations,
such as Fourier transforms (FT), short-term Fourier transforms, and WT, are often used to
Queue
Station 1 Station 2
Active bottleneck
25
process the raw signal to de-noise and obtain underlying frequency information hidden in the raw
signal. Fourier transform is given by the following equation.
Equation (1) represents FT of a raw signal, , that is obtained by multiplying, or
convolving, the signal with an exponential term at a particular frequency, , and integrating it
over time. The resulting spectrum shows the sine-wave frequencies that constitute . Figure
7(a) shows a simple, infinite sinusoidal signal, expressed as
ftx 2sin)(
In the frequency domain, as shown in Figure 7(a), the FT spectrum consists of a single
spectral line, or “spike,” of signal energy with amplitude 1. Thus, the signal has only one rate of
change, namely its sole frequency . However, traffic flow is far from infinitely sinusoidal. A
somewhat more realistic example is steady traffic that may become oscillatory at a point in time,
then even out again. Such a case is drawn in Figure 7(b). Here, the FT produces a broadened
complex spectrum that shows the sine wave’s frequency with other frequencies produced by the
starting and ending of the signal. The FT of the signal gives information about what frequency
components are present over the entire period of signal, but it does not represent what frequency
components exist at a particular time and how they change over time.
Due to this limitation, FT is effective in characterizing a stationary signal, like that of
equation (1a) and Figure 7(a), in which the frequency content does not change over time. Traffic
patterns may be stationary in certain circumstances, but they often exhibit non-stationary
features due to the emergence of stop-and-go traffic, onset of congestion, incidents, work zones,
and so on, and FT may not be effective in decomposing and analyzing them. One cannot get the
(1)
(1a)
26
time-frequency information of the signal using FT as seen in Figure 7(c); hence FT may not be
effective in decomposing and analyzing traffic data.
(a) (b)
(c)
Figure 7. (a) Fourier Transform of a Continuous Sine Wave Signal (b) Fourier Transform of a Finite-Length Sine Wave Signal (c) Single-Frequency Spectral Energy vs. Time of a Finite-Length Sine Wave Signal Unattainable with Fourier Transforms
27
Wavelet transform (WT) is a powerful spectral analysis tool that provides time-frequency
information of the given signal rather than only frequency information as in FT. That is, rather
than providing spectral energies over the entire time period as in Figures 7(a) and 7(b), WT
reveals the signal’s spectral energy over any time period as in Figure 7(c). Thus, WT can
effectively analyze non-stationary signals, such as speed and flow time series.
A wavelet coefficient, , , is a complex mathematical function given by,
φ s, τ | |x t φ ‐ dt
where tx is the raw signal, in this case either speed or flow time-series. is the
transformation function or mother wavelet function. , a real number (Note that a real number
may be an integer or a fraction, but it has no imaginary component as in complex or vector
mathematics), is the time-translation parameter, which determines where the center of the mother
wavelet function is placed along the time-domain graph of the signal. s , a real number that does
not include zero because s appears in a denominator, is the scale parameter that determines the
width of the mother wavelet function. The magnitude of s governs the dilation and contraction
of the mother wavelet function and is defined as the inverse of frequency. That is, high s refers
to low frequencies in the given signal representing non-detailed or global views of the signal. In
contrast, low s refers to high frequencies representing more detailed views of the signal (e.g.,
noise). Because is convolved with a transformation function
s
t that is a function of
both scale (frequency) and time, WT provides the time-frequency information of the non-
stationary signal unlike FT. Without delving into mathematical details, these wavelet coefficients
(spectral energies) of the given signal essentially represent the rates of change of the signal with
time. In theory, the analyst using WT computes the wavelet coefficients by applying equation (2)
(2)
28
for all time translations and all scales s . In practice, however, the , dependent on the data
resolution, are not continuous, and neither are the s . The resulting wavelet coefficients are
therefore considered averages. 20- second detector data (speed/flow) have been used in this
study, and WT is computed for each detector output on a given study day. Thus, as we will see in
the following example, changes in the signal (e.g., a speed drop) generate large absolute values
of wavelet coefficients.
To illustrate the convolution of the signal with the wavelet function
s
t as in
Eq. 2, the top panels of Figure 8 shows a representative raw speed signal with time
represented on the x-axis and speed on the y-axis. However, unlike the top panels of Figures 8,
these signals are each superimposed with two wavelets, the left side with wavelets having s =1
and the right side with wavelets having s =3. Notice that the wavelets with larger s are more
dilated than those with smaller s . Note that the Mexican Hat wavelet is used in this
example (and for our analysis), which is one of several wavelet functions proven effective for a
wide range of signals. The Mexican Hat wavelet function is the negative normalized second
derivative of the Gaussian function and is represented by
Haar, Daubechies, biorthogonal and Meyer are some of the other widely used mother
wavelet functions. The bottom left panel of Figure 8 shows the wavelet coefficients (spectral
energies) that result when the raw signal is convolved with the s =1 wavelet for all using
equation (2). The coefficient value that results when the wavelet passes =15:06 hours is
(3)
29
specially denoted for illustrative purposes, as is that at 15:12 hours. The bottom right panel does
likewise, except that the more dilated wavelet, s =3,is used.
Figure 8 shows the effects of choosing various wavelet dilations. The red wavelet on the
left focuses narrowly on a part of the signal that is changing rapidly at 15:06 hours and thus
produces a relatively large wavelet coefficient. By contrast, the other red wavelet almost fully
envelops the oscillatory part of the signal and renders it as a region with little rate of change,
yielding a low wavelet coefficient. On the other hand, the green wavelet on the left captures only
a small part of a long decline of the signal and thus produces a relatively small wavelet
coefficient. By contrast, the other green wavelet envelops much more of the decline and renders
it as a region with a high rate of change, yielding a high wavelet coefficient. This behavior shows
that the wavelet coefficients for 1s reveal more detailed information of the signal, such as
small local changes and noise on the signal. By contrast, the coefficients with 3s reveal a
more approximate/global trend and expose longer-term changes in traffic flow while suppressing
signal noise.
For a non-stationary signal, which is often the case for speed and flow time series,
wavelet coefficients are computed for a range of scales to represent different frequency
information of the signal. Then, the average coefficients are computed to identify significant
changes, such as a significant speed drop, in the signal. The maximum scale is typically a
function of sample size. Although the wavelet coefficients in Figure 8 are graphed like time-
domain functions along time axes, they are very much like spectral energies shown in Figures
7(a) and 7(b). Each point on a wavelet coefficient trace in the lower half of Figure 7 represents
the tip of a spectral line of at that instant and at a frequency that is the inverse of s from the
mother wavelet’s scale parameter.
30
Figure8. Mexican hat wavelet illustration
There are two types of wavelet transforms, continuous wavelet transforms (CWT) and
discrete wavelet transforms (DWT). In CWT, the scale and translation parameters are
continuous, and thus wavelet coefficients are obtained continuously over and (as in Equation
(Eq.2)), thereby leading to redundancy in the information obtained. This redundancy allows one
to identify event times (e.g., bottleneck activation) more precisely, albeit at the expense of
efficiency. In DWT, the signal is decomposed in a discrete fashion; wavelet coefficients are
computed with discrete values of and . This can be achieved by adjusting the wavelet function
as shown in equation (4).
,| |
0
10
20
30
40
50
60
70
15:00 15:05 15:10 15:15 15:20
Speed (mph)
Time
0
1
2
3
4
5
15:00 15:05 15:10 15:15 15:20
Wavelet Coefficients
Time
Speed
S=1
=15:12=15:06
s s s s
0
2
4
6
8
10
15:00 15:05 15:10 15:15 15:20
Wavelet Coefficients
Time
0
10
20
30
40
50
60
70
15:00 15:05 15:10 15:15 15:20
Speed (mph)
Time
S=3
Speed
=15:06 =15:12
s s s s
(4)
31
Where ∈ 2 , ∙ , , ∈ (Z is set of integers, ≠0 because is in the denominator). In
this case, the initial value of is set to 2 and increased by the power of 2 in the next iterations.
The maximum scale is restricted to the sample size. is a linear function of with as a
multiplying factor. (Note that in certain applications, can be independent of ). DWT
decomposes the signal more efficiently than CWT since the coefficients are computed based on a
subset of and , albeit at the expense of resolution. More importantly, the DWT scheme allows
one to reconstruct the signal via inverse transform, thereby enabling noise filtering. This process
is described below in more detail. In light of the properties of CWT and DWT, DWT is used to
de-noise the raw speed and flow data, and CWT is used to identify the bottleneck activation and
de-activation times and steady-state periods.
Filtering data noise. For the purpose of de-noising, a raw signal, , can be expressed
as
Where is the (discrete) time in equal intervals; is the signal in the absence of noise; is
white noise assumed to be Gaussian distributed, 0, 1 and is the standard deviation. The
goal is essentially to extract from the raw signal. This is achieved by (i) decomposing the
raw signal into different frequency components via DWT, (ii) determining noise components by
applying threshold(s) on the wavelet coefficients, and (iii) reconstructing the signal (without the
noise components) via inverse WT (Misiti et al., 2010). More details of each step follow.
The raw signal is filtered according to the wavelet based subband algorithm; see Figure 9
for the basic principle. (The details of this algorithm are provided in Polikar (2001).) The raw
signal is passed through three levels of high-pass and low-pass filters using the Daubechies
wavelet to decompose the signal into high frequency and low frequency components. In level 1
(5)
32
the signal is decomposed into “detail” wavelet coefficients representing high frequency
components, /2 − , and “approximation” wavelet coefficients representing low
frequency components, 0 − /2, where is the maximum frequency in the raw signal. In
level 2, the low frequency components are again bisected and decomposed into approximation (0
− /4) and detail ( /4 − /2) wavelet coefficients. In level 3, the lowest frequency
components are once again decomposed into approximation (0 − /8) and detail ( /8 −
4) wavelet coefficients. Note that the lowest frequency components are successively passed
through the filters because they have low temporal resolution and are not well represented in the
time domain (Robi and Polikar, 2001). After the three levels of decomposition, wavelet
coefficients representing frequencies of 0 − /8 are considered as approximation wavelet
coefficients and others are considered as level-1, level-2, and level-3 detail coefficients. Noise in
the signal, which typically displays high frequencies, is assumed to be present in the detail
wavelet coefficients.
33
Figure9. Wavelet based the subband algorithm.
Note that the scale parameter and the increment of the translation parameter of the
wavelet function increase by power of 2 to better decompose lower frequency components and
avoid redundancy for efficiency. This means that the sample size decreases by power of 2.
Therefore, the number of decomposition levels depends on the sample size. Three levels of
decomposition were deemed sufficient in the present study.
Once the signal is decomposed, we determine the noise components by applying hard
thresholds ( ’s) on all three-levels of detail wavelet coefficients. Specifically, the wavelet
coefficients below the thresholds are considered high-frequency noise components and are
therefore removed: i.e.,
, | | 0, | |
Raw signal x(t)
AWC- /2
Level 1=2, =2
LP HP
LP HP
LP HP
Level 2=4, =4
Level 3=8, =8
AWC- /4
AWC- /8
DWC/2 -
DWC/4 -
DWC/8 - 4
LP: Low pass filterHP: High pass filter
(6)
34
Where represents detail wavelet coefficients of the raw signal . The threshold
values, ’s, are determined based on the Rigorous SURE method that is found to be most
effective in de-noising real signals (Rosas-Orea et.al., 2005). In this method, is determined as:
2 log log
where is the sample size. Note that since varies with the level, different threshold values are
used for different levels.
Finally, the signal is reconstructed via inverse wavelet transform using the approximation
coefficients and the detail coefficients remaining after removing the noise components.
Examples of de-noised speed and flow data are shown in Figure 10(a) and 10(b), respectively.
(7)
35
(a)
(b)
Figure10. (a) De-noised speed; (b) De-noised flow on 01/08/09, I-10 eastbound, Phoenix.
20
25
30
35
40
45
50
55
60
65
13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00
Spe
ed (
mph
)
Time
Speed De-noised Speed
0
2000
4000
6000
8000
10000
12000
14000
16000
13:0014:0015:0016:0017:0018:0019:0020:00
Flo
w (
veh/
hr)
Time
Flow De-noised Flow
36
Bottleneck activation and discharge rate. Using the de-noised data, the characteristics
of bottlenecks are analyzed. We first identify the times of onset and clearance of queue using the
speed data obtained from measurement location 1 (immediately upstream of the bottleneck).
These times are identified in a systematic manner using CWT and used later to estimate the times
at the downstream measurement location. Among several mother wavelet functions, the Mexican
Hat wavelet is adopted based on the previous finding that it is effective in analyzing traffic data
(Zheng et al., 2011). The Mexican Hat wavelet function is the negative normalized second
derivative of the Gaussian function and is represented by
√ / 1
Based on its shape, the Mexican Hat wavelet generates peaks and dips whenever there are
changes in the signal. In this research, absolute values of wavelet coefficients are used so that
changes in speed or flow correspond to peaks. As shown in Figure 11(a), the onset of congestion
marked by a sharp decrease in speed corresponds to a peak in the (absolute value of) wavelet
coefficients. Note that there is another pronounced peak immediately after the onset of
congestion. This marks the end of transition to the congested regime. Similarly, the clearance of
congestion marked by a recovery in speed also corresponds to a peak. The peak prior to the
clearance represents the start of transition to the free-flow regime. For this example, the start and
the end of congestion are identified to be at 14:42:40 p.m. and 18:52:17 p.m., respectively. The
same technique is used on flow data to identify the periods of near-steady traffic states, in which
the flows remain nearly constant (i.e., the periods between two neighboring peaks in wavelet
coefficients); see Figure 11(b). Specifically, we identify the near steady-state period immediately
(8)
37
before the onset of congestion to measure the pre-congestion congestion flow (to be used in
computing the capacity drop).
(a)
Figure11. (a) Times of queue onset and clearance based on continuous wavelet transform; (b) Near-steady state periods based on continuous wavelet transform (06/06/2008).
0
10
20
30
40
50
60
0
10
20
30
40
50
60
70
14:00 15:00 16:00 17:00 18:00 19:00
Wav
elet
Coe
ffic
ient
s
Sp
eed
(mph
)
Time
Wavelet Coefficients Speed Peaks
Queue onset
Queueclearance
0
5000
10000
15000
20000
25000
30000
-4010000
-3990000
-3970000
-3950000
-3930000
-3910000
14:10 14:20 14:30 14:40 14:50 15:00
Wav
elet
coe
ffic
ient
s
Obl
ique
cum
ulat
ive
flow
N
(t)-
q 0*(
t-t 0
), q
0=10
,500
veh
/hr
Time
Oblique cumulative flow Wavelet coefficients Peaks
20,000 Steady state
38
CHAPTER 4
REGIONAL BOTTLENECK ANALYSIS
The objective of this study is to develop a methodology which could be used efficiently
to identify and analyze freeway bottlenecks in a region in a consistent, reproducible manner. In
recent years, there have been efforts to understand the characteristics of freeway bottlenecks and
found that freeway bottlenecks are observed to exhibit reproducible features even though they
display temporal variations which could be mere stochastic fluctuations or due to changes in
several traffic features like on-ramp flows, lane changing etc. It was found that the bottleneck
discharge rate decreased upon bottleneck activation and thus identifying freeway bottlenecks and
studying the mechanism of their activation and capacity drop are important in improving
operational efficiency and reducing freeway delay. However they are not many efforts to
systematically identify active bottlenecks and measure the capacity drop on a regional network.
Choe et al. (Choe, Skabardonis and Varoaiya, 2002) and Wieczorek et al. (Wiezorek,
Moctezuma and Bertini, 2010) have worked on identifying the bottlenecks at regional level but
in this study a methodology comparable to the rigorous methods was developed to measure
capacity drop and its temporal (day to day variations) and also provide a better understanding of
detailed features of freeway bottlenecks in a region.
To this end, Phoenix metropolitan region has been chosen as the case study site. The
Phoenix metropolitan region has several recurrent bottlenecks, some of which result in long
queues and large delays during rush-hour periods. All Interstates, US Routes and State Routes
with available detector data in the region were analyzed. Recurrent bottleneck locations were
identified based on several criteria including congestion pattern, sensor coverage, data quality
and (absence of) incident/construction activities. Chapter 4 presents the analysis results of all 23
39
bottlenecks identified, including some general observed congestion patterns, affected locations,
number of days observed, and the feasibility of measuring or estimating bottleneck discharge
rates. The identified bottlenecks were ranked according to the capacity drop in terms of flow and
percent reduction in flow. This chapter also presents the comparison of the results obtained using
WT with the result based on the regional analysis of 5-minute data to gauge the trade-off
between precision and efficiency. This research shows that the 5-minute data could be effectively
used in identifying and prioritizing active bottlenecks in a region. However, for studying the
detailed mechanism of the high ranked active bottlenecks identified through the regional analysis
it is advisable to use higher resolution data with an effective de-noising methodology as many
traffic phenomena like lane changing, traffic stationary periods, oscillations etc. occur at a
frequency less than 5 minutes.
Case study site and data
For this study, all interstates (I), US Routes (US), and State Routes (SR) in the Greater
Phoenix area, where detector data are available, were analyzed to identify locations of recurrent
bottlenecks and measure or estimate bottleneck discharge rates. The coverage of traffic sensors is
illustrated in Figure 12 using ArcGIS 9.3. Most freeways and highways are equipped with
inductive loop detectors except for I-17 and SR 51, which are equipped with passive acoustic
detectors (PADs). Six months of data from these detectors were analyzed, spanning from July,
2009 through July, 2010 (though much data after January, 2010 were missing.) The data pro-
vides vehicle counts, time-mean speeds, and occupancies that were aggregated over 5-minute
intervals. We further analyzed a bottleneck using the regional methodology using 5-minute data
which has been described in detail in Chapter 3and compared the results with those based on the
40
wavelet analysis to evaluate the results from the regional-level analysis. The 20-second data were
taken from July, 2008 to March, 2009. In this research, a.m. peak is considered from 6-10 a.m.
and p.m. peak is considered from 3-7 p.m.
Figure12. Map of Greater Phoenix congested freeway segments with coverage of loop detectors and passive acoustic detectors. (Source: Samuelson (2011), Application: ArcGIS 9.3)
Identification of recurrent bottlenecks
In identifying major recurrent bottlenecks, the following criteria were considered:
Congestion Level
Sensor Coverage of the Queue
Data Quality
Non-recurrent congestion
41
Congestion level. In this study, speed below 45 mph is classified as congestion. Ideally, it
should be site-specific but for a regional analysis, a reasonable value was selected based on
examination of speed data from various freeway sections. There are studies that use similar
values (Choe, Skabardonis and Varoaiya, 2002; Wiezorek, Moctezuma and Bertini, 2010). The
sites for which the temporal (>30 minutes) and spatial extent of the congestion are large are
identified. Localized and non-recurrent congestion (these can be due to incidents, weather, etc.)
are not considered for analysis. These sites are identified in the forthcoming figures with the help
of speed contours that represent spatiotemporal distributions of speed in different color schemes.
Sensor coverage of the queue. The head of a queue is the farthest downstream part of the
queue, at the bottleneck, containing vehicles that are discharging from the congested area. The
tail of the queue is the farthest upstream part of the bottleneck, containing vehicles that are
entering the shockwave part of the queue and coming into the congestion. Ideally, the entire
queue fits within the study section with sufficient sensor coverage to measure or estimate
bottleneck discharge rates and queue length. Such an idealization is shown in Figure 13.
In Figure 13, the time-space region is colored according to the speed based on the color
scheme provided in the legend. Dark areas correspond to low speeds, indicating presence of
congestion. However, given the objectives of study, it was not deemed critical to measure the
queue length. Thus, we considered all the sites where the bottleneck discharge rate can be
measured or estimated using the detector data. For example, in Figure 14(a), a queue formed at
bottleneck 3 (labeled as “BN 3”) and propagated beyond MP160.23. Thus, the queue length
cannot be measured. Nevertheless, it is still possible to measure or estimate the bottleneck
discharge rate around MP 152. On the other hand, if a bottleneck location resides downstream of
the detector coverage region, the bottleneck discharge rate cannot be measured or estimated; see
42
Figure 14(b). Of note, it was common to observe multiple bottlenecks on a study corridor; and
often times, a bottleneck was “de-activated” due to the spill-over of a downstream queue. Figure
14(a) illustrates three major bottlenecks, two of which (BN 1 and 2) were de-activated due to the
queues from the downstream bottlenecks (BN 2 and 3, respectively). In such circumstances, the
most downstream bottleneck (BN 3 in Figure 14(a)) was analyzed where the discharge rate can
be measured consistently throughout the time.
Figure 13. Speed contour plot from Matlab of ideally located bottleneck having entire queue contained within detector coverage area.
43
(a)
(b)
Figure14. (a)Tail of a queue not contained within the detector coverage area. (I-10 WB AM peak) (b) Head of a queue not contained within the detector coverage area (Loop 202 WB a.m. peak)
44
Data. To obtain meaningful results, the following procedure was implemented to assess the
quality of data and take appropriate actions:
Days with a majority of missing data were excluded from the analysis.
Days with a significant amount of missing data in congested time-space regions were used only
for classifying congestion patterns (e.g., bottleneck locations) but not for quantitative analysis of
capacity drop and performance statistics (e.g., VMT and VHT).
For the remaining days in which quantitative analyses were performed, further assessment
of data quality was performed as follows.
If a significant amount of data was missing in uncongested time-space regions, the
missing data were imputed using the valid data from neighboring detectors.
Erroneous data were identified using the following filtering criteria established by TTI
(Turner, Margiotta and Lomax 2004) and replaced by an average of the two nearest
valid data points in time (one preceding and one following the time of interest, not
exceeding 15 minutes):
5-minute flow < 3,060 vph
Speed < 100 mph
Speed > 5 mph and 5-minute flow > 0
45
Non-recurrent congestion. Ideally, days with incidents and work zones can be identified
from the archives (e.g., highway condition reports). Alternatively, days with recurrent congestion
can be identified conveniently from speed contour plots, as exemplified in Figure 14. For our
analysis, we selected the days for which the congestion/spatial extent of the queue were
relatively consistent. The recurrent congestion pattern for I-10 eastbound during p.m. peak is
shown in Figure 15(a). The bottleneck around MP 154.63 activates around 3:20 p.m. and remains
active until 7 p.m., resulting in a 6.7-mile-long queue. This pattern was prevalent on the selected
study days. In this research, we define recurrent congestion as a freeway condition in which the
travel demand exceeds the freeway capacity resulting in congestion (below 45 mph) for 30
minutes of longer on an incident-free weekday. In contrast, Figure 15(b) represents a day with
non-recurrent congestion, in which a much longer queue is observed due to an obvious
restriction around MP 141.826. This non-recurrent congestion could be attributed to accidents,
breakdowns, construction, or inclement weather.
46
(a)
(b)
Figure 15. (a) Speed contour for the day with recurrent congestion on I-10 EB. (p.m. peak) (b) Speed contour for the day with non-recurrent congestion on I-10 EB. (p.m. peak)
47
Evaluation of regional analysis
Bottleneck mechanism is studied in detail based on the WT technique described in
Chapter 3 using 20-second data for the I-10 eastbound bottleneck between S. 53rd St. and W.
Southern Ave. The period of analysis is from July 2008 to March 2009. The selected site is a
weaving bottleneck due to a busy on-ramp from W. Broadway Rd. with an average flow of 1,454
vph during congestion and a major exit to US-60 eastbound with an average flow of 5,205 vph
during congestion; see Figure 16 for the schematic of the site. The analysis results are shown in
Table 1. Bottleneck activation times are fairly consistent, varying from 14:31 p.m. to 14:51 p.m.
However, bottleneck de-activation times varied to a larger degree from 16:38 p.m. to 18:48 p.m.
The pre-congestion flow ranged from 10,616 to as high as 12,442 vph, whereas the average flow
during congestion varied from 9,746 to 10,765 vph. As a result, the capacity drop varied from 3
to 17 percent.
Figure 16. Schematic of I-10 eastbound bottleneck
We further analyzed the same bottleneck for the same period based on the simple method
using 5-minute data which has been described in detail in Chapter 3.1 and compared the results
Approximate Bottleneck Location
Det#55MP 152.410
E. Jefferson St. Sky Harbor Blvd.
E. Buckeye Rd. I‐17 S. 24th St. E. University Dr.
S. 40th St. S. 48th St. W. Broadway Rd. US‐60 EB
US‐60 EB, HOV
Det#149MP 148.577
Det#93MP 149.167
Det#40MP 150.241
Det#46MP 151.101
Det#50MP 151.656
Det#393, MP 154.630
Det#64, MP 153.539
Det#59MP 152.992
48
with those based on the wavelet analysis to evaluate the results from the regional-level analysis.
More specifically, the pre-congestion flow was measured by taking the maximum 5-minute flow
within 30 minutes prior to the bottleneck activation. The bottleneck discharge rate during
congestion was measured by taking the average of all 5-minute flows during congestion.
Reasonably close results would justify the implementation of the simpler analysis in favor of
efficiency. The results based on the regional analysis are shown in Table 2. It is notable that the
ranges of the reported values are fairly close to those in Table 1, although some daily differences
are apparent.
Table 3 and Figure 17 present the summary of the comparison result. The average
bottleneck activation and de-activation times are fairly comparable between the two methods,
especially given the difference in the data resolution (5 minutes vs. 20-second). The average
values of both pre-congestion and congestion flows are slightly higher in the wavelet analysis
than in the simple analysis;. Finally, there is little difference in the average capacity drop (~11
percent) between the two methods. In summary, the results obtained from the two methods are
similar on average, which justifies the use of the simple method for the regional analysis.
However there is a systematic underestimation of pre-queue flow and discharge rate with the
simple method underlying the importance WT based analysis for detailed analysis. The regional
analysis underestimates both the pre-activation flow and average congestion flow by around 3%.
49
Table 1. Results: bottleneck analysis using wavelet analysis.
DateBN
activation time
BN deactivatio
n time
Pre-activation flow (vph)
Average congestion flow (vph)
Capacity drop
(percent)
6/3/2008 14:45:27 18:09:45 11,435 10,516 8.04
6/4/2008 14:40:47 18:26:25 12,127 10,321 14.89
6/6/2008 14:39:47 17:47:05 11,859 10,358 12.65
6/11/2008 14:39:34 18:13:14 10,894 10,360 4.9
7/9/2008 14:44:18 18:21:56 10,616 10,345 2.55
7/11/2008 14:42:58 17:33:56 11,904 10,174 14.54
7/30/2008 14:42:58 18:26:35 11,564 10,055 13.05
8/6/2008 14:43:38 18:34:15 11,945 9,872 17.35
8/8/2008 14:30:38 17:47:16 11,432 10,128 11.41
8/13/2008 14:44:58 18:23:36 11,798 10,416 11.71
8/29/2008 14:42:45 17:13:45 11,307 10,541 6.77
9/3/2008 14:40:18 18:39:35 12,442 10,456 15.96
9/15/2008 14:46:36 17:45:36 11,315 10,743 5.05
9/16/2008 14:45:56 18:35:56 11,618 10,419 10.33
9/19/2008 14:45:09 17:18:07 11,589 10,578 8.72
10/6/2008 14:48:09 18:22:47 11,697 10,410 11
10/8/2008 14:48:09 18:21:07 12,172 10,399 14.57
10/9/2008 14:48:49 18:14:07 11,549 10,609 8.14
10/20/2008 14:50:16 17:54:36 12,090 10,526 12.94
11/3/2008 14:43:49 17:19:07 11,784 10,722 9.01
11/4/2008 14:40:49 18:14:27 11,754 10,505 10.63
11/10/2008 14:45:49 17:19:47 11,422 10,656 6.71
11/12/2008 14:40:29 16:37:48 11,988 10,765 10.2
11/20/2008 14:42:20 18:00:18 11,557 10,193 11.8
11/24/2008 14:45:27 17:30:27 11,876 10,619 10.59
12/3/2008 14:50:47 17:33:47 11,737 10,406 11.35
12/15/2008 14:44:00 18:39:17 10,976 9,746 11.21
12/17/2008 14:39:40 18:39:17 11,465 10,287 10.28
1/5/2009 14:44:00 18:21:37 11,940 10,656 10.76
1/7/2009 14:44:40 18:47:37 12,098 10,230 15.44
1/8/2009 14:48:20 18:37:37 11,436 10,205 10.76
1/13/2009 14:42:40 18:42:17 11,537 10,043 12.94
1/23/2009 14:46:00 18:28:37 12,220 10,376 15.1
50
Table 2.
Results: bottleneck analysis using regional analysis.
DateBN
activation time
BN deactivatio
n time
Pre-activation flow (vph)
Average congestion flow (vph)
Capacity drop
(percent)
6/3/2008 14:35:00 18:10:00 10,488 10,363 1.19
6/4/2008 14:35:00 18:25:00 10,920 10,210 6.5
6/6/2008 14:40:00 17:50:00 11,784 10,194 13.5
6/11/2008 14:35:00 18:05:00 10,824 10,240 5.4
7/9/2008 14:35:00 18:15:00 10,344 10,264 0.77
7/11/2008 15:10:00 17:50:00 10,812 10,066 6.9
7/30/2008 15:10:00 18:35:00 11,772 9,917 15.76
8/6/2008 15:05:00 18:40:00 12,060 9,643 20.04
8/8/2008 14:40:00 17:55:00 10,812 9,987 7.63
8/13/2008 15:15:00 18:25:00 11,100 10,230 7.83
8/29/2008 14:40:00 17:15:00 11,028 10,457 5.18
9/3/2008 15:40:00 18:40:00 11,304 10,233 9.48
9/15/2008 15:10:00 18:05:00 11,124 10,578 4.91
9/16/2008 14:40:00 18:35:00 11,832 10,270 13.2
9/19/2008 15:10:00 18:00:00 11,388 10,246 10.03
10/6/2008 15:35:00 18:15:00 11,148 10,246 8.09
10/8/2008 15:10:00 18:40:00 11,928 10,019 16
10/9/2008 15:10:00 18:25:00 11,556 9,993 13.53
10/20/2008 15:15:00 18:40:00 11,964 10,131 15.32
11/3/2008 15:10:00 18:30:00 11,208 10,288 8.21
11/4/2008 14:35:00 18:30:00 11,436 10,225 10.59
11/10/2008 15:15:00 18:05:00 10,872 10,324 5.04
11/12/2008 14:55:00 19:00:00 11,880 9,659 18.69
11/20/2008 15:00:00 19:00:00 11,652 9,456 18.85
11/24/2008 15:05:00 18:35:00 11,616 10,222 12
12/3/2008 14:45:00 19:00:00 11,820 9,577 18.98
12/15/2008 14:40:00 18:45:00 11,028 9,331 15.39
12/17/2008 14:40:00 18:45:00 11,532 9,941 13.8
1/5/2009 15:10:00 18:30:00 12,780 10,482 17.98
1/7/2009 15:10:00 18:45:00 11,664 10,079 13.59
1/8/2009 15:10:00 18:50:00 11,520 10,038 12.86
1/13/2009 14:40:00 18:50:00 11,400 9,896 13.19
1/23/2009 14:35:00 18:35:00 10,896 10,234 6.08
51
Table 3.
Comparison of wavelet analysis and simpler analysis.
Wavelet analysis Simpler analysis
No. of days 33 33
Data resolution 20-second data 5-min data
Average BN activation time 2:43:56 p.m. 2:57:35 p.m.
Average BN de-activation time 6:05:30 p.m. 6:26:13 p.m.
Average pre-congestion flow (VPH) 11671 11379
Average congestion flow (VPH) 10383 10092
Average capacity drop (percent) 10.95 11.11
(a)
Figure 17. Comparison of wavelet and regional analysis (a) average congestion flow (b) pre-activation flow
9,200
9,400
9,600
9,800
10,000
10,200
10,400
10,600
10,800
11,000
9,200 9,400 9,600 9,800 10,000 10,200 10,400 10,600 10,800 11,000
Ave
rage
con
gest
ion
flo
w (
vph
), r
egio
nal a
nal
ysis
Average congestion flow (vph), wavelet analysis
52
(b)
Figure 17(contd.). Comparison of wavelet and regional analysis (a) average congestion flow (b) pre-activation flow
Regional bottleneck analysis
In this study, 23 bottlenecks that recurred during morning and evening peak hours were
identified. Of these 23 recurrent bottlenecks 13 bottlenecks were selected based on the selection
criteria discussed in the Chapter 4.2. These bottlenecks were attributed to a variety of factors,
such as merging at busy on-ramps or freeway-to-freeway connectors, weaving due to busy
merges followed by busy diverges (especially near major freeway-to-freeway interchanges), and
curves. Tables 4 and 5 show the recurrent bottlenecks identified during a.m. and p.m. peak hours
in the Phoenix metropolitan region.
10,000
10,500
11,000
11,500
12,000
12,500
13,000
10,000 10,500 11,000 11,500 12,000 12,500 13,000
Ave
rage
pre
-act
ivat
ion
flo
w (
vph
), r
egio
nal
an
alys
is
Average pre-activation flow (vph), wavelet analysis
53
Table 4.
Recurrent congestion identified during a.m. peak hours (6 - 10 a.m.).
ID Route Bottleneck location
No of days observed
(out of 131 weekdays)
Bottleneck discharge rate
A1 I-10 EB MP:146.058-147.332, b/w N.9th
St. & 19th St. 90 Estimated
A2-1 I-10 WB MP: 154.89-154.259, b/w Meadowclark Cir. & W.
Alameda Dr. 44 Measured
A2-2 I-10 WB MP: 152.248-151.473, b/w S. 32nd
St. & S. 31st St. 68 Estimated
A2-3 I-10 WB MP: 155.54-154.89, b/w W.
Donner Dr. & Meadowclark Cir.
29 Measured
A3 I-17 SB MP: 204.71-203.7, b/w W. Solano Dr. & W. Elm Dr.
42 Estimated
A4-1 L-101 NB MP: 58.34-57.46, b/w W.
Palomino Dr. & W. Newton Ct. 11
Not measured or estimated
A4-2 L-101 NB MP: 57.46-55.88, b/w E. Newton
Ct. & E. Watson Dr. 63
Not measured or estimated
A5-1 L-202 WB MP: 7.509-6.299, b/w E. Newton
Ct. & E. Watson Dr. 78 Estimated
A5-2 L-202 WB d/s of 0.578, d/s of N.22 St. 58 Not measured or
estimated
A6-1 SR-51 SB MP: 6.16-5.48, b/w E. Northern
Ave. & E. Lamar Rd. 33 Estimated
A6-2 SR-51 SB MP: 2.53-1.32, b/w E. Amelia
Ave. & E. Virginia Ave. 56 Estimated
A7 US-60 WB d/s of 172.37, d/s of S. Albert
Ave. 63
Not measured or estimated
54
Table 5.
Recurrent congestion identified during p.m. peak hours (3 - 7 p.m.).
ID Route Bottleneck location
No of days observed
(out of 131 weekdays)
Bottleneck discharge rate
P1-1 I-10 EB MP: 153.539-154.63, b/w S. 53rd
St. & W. Southern Ave. 87 Estimated
P1-2 I-10 EB d/s of MP:160.25, d/s of E. Gold
Poppy Way 84
Not measured or estimated
P2 I-10 WB MP:140.524-139.524, b/w N. 44th
Ave. & N. 52nd Ave. 50 Estimated
P3 I-17 NB d/s of MP: 208.69, d/s of W. Beryl
Ave. 70
Not measured or estimated
P4-1 L-101 SB MP: 53.784-54.49, b/w E. Golf
Ave. & US-60 38 Estimated
P4-2 L-101 SB MP: 56.08-56.8, b/w E. Pegasus
Dr. & E. Tempe Water Trmt.Drwy 68 Estimated
P5 L-202 WB d/s of MP: 0.579, d/s of N. 22nd St. 57 Not measured or
estimated
P6-1 SR-51 NB MP: 2.71-3.97, b/w E. Devonshire
Ave. & E. Georgia Ave. 21 Estimated
P6-2 SR-51 NB MP: 4.82-5.8, b/w E. Keim Dr. &
E. Aurelius Ave. 41
Could not be analyzed
P6-3 SR-51 NB MP:1.79-2.71, b/w E. Avalon Dr.
& E. Devonshire Dr. 43
Not measured or estimated
P7 US-60 EB MP:172.65-175.45, b/w S. Shafer
Dr. & S. Kachina Dr. 90
Not measured or estimated
The following performance measures are reported in these sections for each recurrent
congestion location identified in Tables 4 and 5:
Duration of congestion (minutes)
Length of congestion (miles)
VMT (for the entire detector coverage area during the peak hour)
VHT (for the entire detector coverage area during the peak hour)
If bottleneck discharge rates can be measured directly or estimated (Chapter 3, Figure 4)
55
o Bottleneck discharge rates and speeds before and during congestion
o Amount and percentage of a reduction in bottleneck discharge rate during
congestion
If bottleneck discharge rates cannot be measured (Chapter 3, Figure 5)
o Flows and speeds before and during congestion at the nearest detector station
upstream of a bottleneck
Note that VMT and VHT for each freeway are computed using the following equations.
I
n
iiLcVMT
1
n
i i
ii v
LcVHT
1
where n represents the total number of detector stations on a freeway; ci represents vehicle
counts (for all lanes) at detector station i; Li represents the length of station i’s influence area;
and vi represents time-mean speed across all lanes, where vi is given by
m
kki v
mv
1
1
where m is the number of vehicles k passing the station’s influence area. The influence area of a
detector station is defined as the area bounded by the midpoints to neighboring detector stations.
We assumed that traffic conditions measured from a detector station were representative of
conditions within its influence area.
The results of the regional analysis have been tabulated in Table 6.
(9)
(10)
(11)
56
Conclusion
The objective of this chapter is to apply the regional methodology which was described in
detail in the previous chapter to both identify and analyze freeway bottlenecks in a region. The
Phoenix metropolitan region has been chosen as the case study site. To this end, all Interstates,
US Routes and State Routes with available detector data were analyzed. Recurrent bottleneck
locations were identified based on several criteria including congestion pattern, sensor coverage,
data quality and (absence of) incident/construction activities.
Bottleneck features were studied by measuring bottleneck activation and de-activation
times, pre-congestion and congestion flows, and capacity drop. For a select bottleneck (the
bottleneck on I-10 eastbound between S. 53rd St. and W. Southern Ave.), two methods were
employed: a sophisticated method based on wavelet transform (WT) on 20-second data to
improve precision and accuracy (at the expense of efficiency) and a simple, automated method
using 5-minute data to improve efficiency (at the expense of precision and accuracy). The WT-
based method was employed to de-noise the detector data and identify key event times such as
the times of congestion onset and change in near steady state flow. With the simpler method,
congestion was defined as speed below 45 mph, and 5-minute data were used instead of
identifying times of flow change. It was found that the two methods generated comparable
results, justifying the use of the simpler method for efficiency without much loss of accuracy.
Based on the above finding, the regional analysis was conducted using the simple
method. Throughout the Phoenix region, 23 recurrent bottlenecks were identified: 12 during a.m.
peak hours and 11 during p.m. peak hours. Of these 23 recurrent bottlenecks, 13 bottlenecks
were selected for bottleneck performance analysis based on the selection criteria discussed in
Chapter 4.2. Most of these bottlenecks were attributed to heavy merging and weaving. For these
57
bottlenecks, a number of performance measures were obtained, such as the duration of
congestion, length of the congestion, VMT, VHT, and bottleneck discharge rate (where it can be
measured or estimated). Bottleneck discharge rates were measured directly at 2 locations and
estimated (using ramp counts) at 11 locations. Due to the limited sensor coverage, the bottleneck
discharge rate could not be measured or estimated for the other 10 bottlenecks. Although these
bottlenecks did not meet our selection criteria, congestion flows at the nearest detector station
upstream of the bottleneck were provided instead along with other performance measures. The
identified bottlenecks were ranked according to the capacity drop in terms of flow and percent
reduction in flow.
58
Avg.
Std. Er
Avg.
Std. Er
Avg.
Std. ErAvg.Std. ErAvg.Std. Er
Avg.
Std. Er
Avg.
Std. Er
Avg.
Rank
Avg.
Rank
A6-
1SR
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SB
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imat
ed75
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1P
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1 N
BE
stim
ated
51.9
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576
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555
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369
0,87
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13
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2P
4-1
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stim
ated
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665
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3A
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795.
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ated
427.
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243
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573
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561
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639
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250
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554,
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944
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68
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56
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imat
ed41
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481
375,
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5453
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542
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534
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69
13.9
7P
1-1
I-10
EB
Est
imat
ed19
9.7
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994
8,58
565
55.5
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6822
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61,
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327
16,2
921,
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.78
A2-
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BM
easu
red
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747
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,756
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1,75
016
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red
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769
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1,26
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2-2
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stim
ated
36.8
5.2
8,47
615
77,
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149
55.9
0.7
41.3
0.6
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67,7
3926
1,00
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6,26
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9.2
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4-2
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stim
ated
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I-10
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Mea
sure
d75.9
9.4
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3831
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--
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BN
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imat
ed85
6.9
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59.9
0.1
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01,
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158
7,22
3-
--
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Not
Mea
sure
d/E
stim
ated
72.2
12.5
5,54
711
14,
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132
63.6
1.6
61.1
2.4
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41,2
5036
8,65
81,
488,
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28,3
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ot M
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imat
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738
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1,12
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911
,711
--
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BN
ot M
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red/
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imat
ed19
9.2
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764
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373,
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11,4
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--
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6-3
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1 N
BN
ot M
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red/
Est
imat
ed82
.77.
15,
850
434,
453
115
58.2
0.4
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0.8
38,9
37,4
1717
6,94
364
1,91
65,
311
--
--
P7
US-
60 E
BN
ot M
easu
red/
Est
imat
ed15
0.2
8.4
6,25
444
4,43
561
55.8
0.3
19.2
0.9
62,0
68,8
3750
6,73
51,
122,
827
9,91
9-
--
-
Throughput
Reduction (%)
Pre‐
Congestion
Speed
(mph)
Congestion
Speed
(mph)
Throughput
Reduction (vph)
VMT
VHT
IDR
oute
Bot
tlene
ck T
hrou
ghpu
tDuration
Pre‐
Congestion
Flow (vph)
Congestion
Flow (vph)
Tab
le 6
. R
egio
nal B
ottl
enec
k A
naly
sis.
59
CHAPTER 5
FREEWAY WEAVING BOTTLENECK: BOTTLENECK FEATIRES AND THE
SMOOTHING EFFECT OF THE HOV LANE
This study analyzed the characteristics of a freeway weave bottleneck with a HOV lane.
Previous studies suggested that lane-changes, induced by merging and diverging flows, diminish
the bottleneck discharge rate and that the activation of a HOV lane can remedy this impact by
discouraging disruptive lane-changes. These previous studies primarily analyzed the smoothing
effect on merge and curve bottlenecks. The present study corroborates the existence of
smoothing effect on a weave bottleneck. Most previous studies on bottlenecks analyze few days
of data, neglect steady-state periods, or fall short of characterizing steady-state periods in a
systematic, reproducible manner.
In this study 33 days of data had been analyzed using a spectral analysis tool called
wavelet transform to systematically de-noise the raw data, unveil underlying trends, and identify
times of queue onset and steady-state periods. From this study we found that: (i) a higher (lower)
flow can be sustained prior to traffic breakdown with higher diverging (merging) flow,
suggesting that ramp-to-freeway maneuvers are more disruptive; (ii) higher bottleneck discharge
rates are attained with higher diverging flow and lower utilization of HOV lane. The latter
indicates that a smoothing effect exists around a weave bottleneck; and importantly, the
smoothing effect was more significant than the effect of diverging flow. By knowing the
bottleneck mechanism it would enable one to fine tune current traffic controls to improve the
bottleneck discharge rate on the freeways.
Data obtained near a freeway weave bottleneck show that the bottleneck discharge rate
diminished by 3-22% upon queue formations. The discharge rate, however, recovered upon the
60
high-occupancy-vehicle (HOV) lane activation, confirming the existence of the “smoothing
effect.” The recovery was substantial; the discharge rate improved by 4% and occasionally
exceeded the maximum pre-queue flow. The smoothing effect persisted for about 1.5 hours and
waned thereafter as the relative utilization of the HOV lane gradually recovered. A statistical
analysis corroborates that the HOV lane flow distribution significantly (and negatively) affects
the bottleneck discharge rate, more so than the amount of diverging flow.
Site and data
The selected study site is an eastbound section of Interstate 10, located between
Broadway Rd. and eastbound US 60 in the Phoenix metropolitan area; see Figure 18(a). This
section of freeway is approximately one mile long and has five regular-use lanes that split into
three exit lanes (to US 60) and three continuing lanes. The site also contains a HOV lane that
splits into an exit lane (to US 60) and a continuing lane. Two or more passengers are required for
the vehicles traveling in the HOV lane during peak hours (6-9 a.m. and 3-7 p.m.). Note that with
the dedicated HOV exit lane to US 60, we expect very few lane-changes from the HOV lane to
the exit lanes. A recurrent bottleneck (Figure 18(b)) resides in this freeway section presumably
due to heavy weaving maneuvers induced by high merging flows from the Broadway Rd. on-
ramp (>1,400 veh/hr during peak hours) and high diverging flows to US 60 (>3,500 veh/hr
during peak hours), often resulting in queues exceeding 5 miles. A typical speed contour is
shown in Figure 18(c).
61
(a)
(b)
Figure 18. (a) Schematic of the study site at I-10 EB, Phoenix, AZ (b) Location of recurrent bottleneck on I-10 EB, Phoenix AZ (c) Typical speed contour of recurrent congestion (I-10 EB)
US 60E
US 60EBroadway Rd.
Lane 1Lane 2Lane 3
Measurement location 1
Measurement location 2~ 1 mile
Approximate Bottleneck Location
Det#55MP 152.410
E. Jefferson St. Sky Harbor Blvd.
E. Buckeye Rd. I‐17 S. 24th St. E. University Dr.
S. 40th St. S. 48th St. W. Broadway Rd. US‐60 EB
US‐60 EB, HOV
Det#149MP 148.577
Det#93MP 149.167
Det#40MP 150.241
Det#46MP 151.101
Det#50MP 151.656
Det#393, MP 154.630
Det#64, MP 153.539
Det#59MP 152.992
62
(c)
Figure 18 (contd.). (a) Schematic of the study site at I-10 EB, Phoenix, AZ (b) Location of recurrent bottleneck on I-10 EB, Phoenix AZ (c) Typical speed contour of recurrent congestion (I-10 EB)
Data come from two measurement locations, as labeled in Figure 1, and consist of vehicle
count, occupancy (dimensionless measure of density) and time-mean speed aggregated over 20-
second intervals. Data from 33 days between July 2008 and February 2009 were analyzed when
the study section was free of reported incidents and adverse weather conditions, and was an
active bottleneck; i.e., traffic was freely flowing at the downstream measurement location
(location 2 in the figure) whereas it was congested at the upstream location (location 1). On
these days, queues consistently formed around 2:40 p.m. and persisted for at least three hours.
Bottleneck discharge flows and off-ramp flows were taken at measurement location 2, and on-
ramp flows were taken at measurement location 1.
63
Bottleneck activation and discharge rate
In this research, the wavelet transform (WT) is used to de-noise the raw data, precisely
identify bottleneck activation and deactivation times, and measure pre-congestion and congestion
flows. These events are typically marked by sharp changes in speed and/or flow, which can be
detected effectively by WT. Please note that some text in this section is a repetition from Chapter
3 but has been included here for the convenience of the readers.
Using the de-noised data (obtained from DWT analysis described in Chapter 3), the
characteristics of bottlenecks are analyzed. We first identify the times of onset and clearance of
queue using the speed data obtained from measurement location 1 (immediately upstream of the
bottleneck). These times are identified in a systematic manner using CWT and used later to
estimate the times at the downstream measurement location. Among several mother wavelet
functions, the Mexican Hat wavelet is adopted based on the previous finding that it is effective in
analyzing traffic data (Zheng et al. 2011). The Mexican Hat wavelet function is the negative
normalized second derivative of the Gaussian function and is represented by
√ / 1
Based on its shape, the Mexican Hat wavelet generates peaks and dips whenever there are
changes in the signal. In this research, absolute values of wavelet coefficients are used so that
changes in speed or flow correspond to peaks. As shown in Figure 19(a), the onset of congestion
marked by a sharp decrease in speed corresponds to a peak in the (absolute value of) wavelet
coefficients. Note that there is another pronounced peak immediately after the onset of
congestion. This marks the end of transition to the congested regime. Similarly, the clearance of
congestion marked by a recovery in speed also corresponds to a peak. The peak prior to the
(12)
64
clearance represents the start of transition to the free-flow regime. For this example, the start and
the end of congestion are identified to be at 14:42:40 p.m. and 18:52:17 p.m., respectively. The
same technique is used on flow data to identify the periods of near-steady traffic states, in which
the flows remain nearly constant (i.e., the periods between two neighboring peaks in wavelet
coefficients); see Figure 19(b). Specifically, we identify the near steady-state period immediately
before the onset of congestion to measure the pre-congestion congestion flow (to be used in
computing the capacity drop).
65
(a)
(b)
Figure 19. (a) Times of queue onset and clearance based on continuous wavelet transform; (b) Near-steady state periods based on continuous wavelet transform (06/06/2008).
However, bottleneck de-activation times varied to a larger degree from 16:38 p.m. to
18:48 p.m. The pre-congestion flow ranged from 10,616 to as high as 12,442 vph, whereas the
average flow during congestion varied from 9,746 to 10,765 vph. As a result, the capacity drop
varied from 3 to 17 percent as shown in Table 7.
0
10
20
30
40
50
60
0
10
20
30
40
50
60
70
14:00 15:00 16:00 17:00 18:00 19:00
Wav
elet
Coe
ffic
ient
s
Spe
ed (
mph
)
Time
Wavelet Coefficients Speed Peaks
Queue onset
Queueclearance
0
5000
10000
15000
20000
25000
30000
-4010000
-3990000
-3970000
-3950000
-3930000
-3910000
14:10 14:20 14:30 14:40 14:50 15:00W
avel
et c
oeff
icie
nts
Obl
ique
cum
ulat
ive
flow
N
(t)-
q 0*(
t-t 0
), q
0=10
,500
veh
/hr
Time
Oblique cumulative flow Wavelet coefficients Peaks
20,000 Steady state
66
Table 7.
Results: bottleneck analysis using wavelet analysis.
The same technique is used on flow data to identify the periods of near-steady traffic
states, in which the flows remain nearly constant; see Figure 19(b) for an example. In the figure,
the top curve is the oblique cumulative count curve constructed by taking cumulative vehicle
DateBN
activation time
BN deactivatio
n time
Pre-activation flow (vph)
Average congestion flow (vph)
Capacity drop
(percent)
6/3/2008 14:45:27 18:09:45 11,435 10,516 8.04
6/4/2008 14:40:47 18:26:25 12,127 10,321 14.89
6/6/2008 14:39:47 17:47:05 11,859 10,358 12.65
6/11/2008 14:39:34 18:13:14 10,894 10,360 4.9
7/9/2008 14:44:18 18:21:56 10,616 10,345 2.55
7/11/2008 14:42:58 17:33:56 11,904 10,174 14.54
7/30/2008 14:42:58 18:26:35 11,564 10,055 13.05
8/6/2008 14:43:38 18:34:15 11,945 9,872 17.35
8/8/2008 14:30:38 17:47:16 11,432 10,128 11.41
8/13/2008 14:44:58 18:23:36 11,798 10,416 11.71
8/29/2008 14:42:45 17:13:45 11,307 10,541 6.77
9/3/2008 14:40:18 18:39:35 12,442 10,456 15.96
9/15/2008 14:46:36 17:45:36 11,315 10,743 5.05
9/16/2008 14:45:56 18:35:56 11,618 10,419 10.33
9/19/2008 14:45:09 17:18:07 11,589 10,578 8.72
10/6/2008 14:48:09 18:22:47 11,697 10,410 11
10/8/2008 14:48:09 18:21:07 12,172 10,399 14.57
10/9/2008 14:48:49 18:14:07 11,549 10,609 8.14
10/20/2008 14:50:16 17:54:36 12,090 10,526 12.94
11/3/2008 14:43:49 17:19:07 11,784 10,722 9.01
11/4/2008 14:40:49 18:14:27 11,754 10,505 10.63
11/10/2008 14:45:49 17:19:47 11,422 10,656 6.71
11/12/2008 14:40:29 16:37:48 11,988 10,765 10.2
11/20/2008 14:42:20 18:00:18 11,557 10,193 11.8
11/24/2008 14:45:27 17:30:27 11,876 10,619 10.59
12/3/2008 14:50:47 17:33:47 11,737 10,406 11.35
12/15/2008 14:44:00 18:39:17 10,976 9,746 11.21
12/17/2008 14:39:40 18:39:17 11,465 10,287 10.28
1/5/2009 14:44:00 18:21:37 11,940 10,656 10.76
1/7/2009 14:44:40 18:47:37 12,098 10,230 15.44
1/8/2009 14:48:20 18:37:37 11,436 10,205 10.76
1/13/2009 14:42:40 18:42:17 11,537 10,043 12.94
1/23/2009 14:46:00 18:28:37 12,220 10,376 15.1
67
counts and subtracting background reductions of to better reveal changes in flow
(i.e., slope) (Munoz and Daganzo, 2002), where is the background flow and is the
elapsed time since reference time . The bottom curve represents the wavelet coefficients. It is
clear that the peaks in wavelet coefficients correspond to the times of significant changes in
flow; therefore, the period between two neighboring peaks is identified as a near-steady state.
On each study day, a surge in freeway flow, accompanied by surges in on-ramp and off-
ramp flows preceded the onset of queue; see Figure 20 for an example. Specifically, queues
consistently formed on the study days when the on-ramp and off-ramp flows exceeded 1,300
veh/hr and 2,600 veh/hr respectively. Thus, the evidence suggests that weaving activities induced
by merging and diverging flows instigated queue formations at this site. Thereafter the
bottleneck discharge rate diminished by nearly 3-22% immediately after the onset (referred to as
the “immediate” reduction in bottleneck discharge rate). The discharge flow partly recovered but
largely remained lower than the flow prior to the onset. (Based on this property, the time of flow
drop is taken as the time of queue onset at the downstream measurement location.) The overall
amount of reduction is measured by taking the difference between the steady-state flow
immediately prior to the onset (referred to as the pre-queue flow hereafter) and the average flow
during congestion.
68
Figure 20. Surges in on-ramp and off-ramp flows around the onset of queue.
Table 8 presents the basic statistics for the times of onset and clearance of queue, pre-
queue flow, the overall reduction in bottleneck discharge rate, and the immediate reduction in
bottleneck discharge rate over the 33 days analyzed. The times of onset of queue are fairly
consistent, varying only from 14:30 to 14:51. However, times of queue clearance vary to a larger
degree from 16:37 to 18:47. The average pre-queue flow and bottleneck discharge rate are
respectively 11,671 veh/hr and 10,383 veh/hr, resulting in the average reduction of 10.95%. The
immediate reduction is larger than the overall reduction at 13.54%.
0
500
1000
1500
2000
2500
3000
3500
4000
14:00 14:10 14:20 14:30 14:40 14:50 15:00
Flo
w (
veh/
hr)
Time
On-ramp flow Off-ramp flow
Queue onset
69
Table 8.
Statistics of bottleneck capacity drop using wavelet analysis.
Average (standard error)
No. of days 33
Time of onset of queue 14:30 – 14:51
Time of clearance of queue 16:37 – 18:47
Pre-queue flow (veh/hr) 11,671 (393)
Bottleneck discharge rate (veh/hr) 10,383 (242)
Reduction in bottleneck discharge rate (veh/hr) 1,288 (74) Reduction in bottleneck discharge rate (%) 10.95 (4)
Immediate reduction in bottleneck discharge rate (veh/hr) 1,592 (99)
Immediate reduction in bottleneck discharge rate (%) 13.54 (5)
Variation in bottleneck discharge rate reduction
We further find that the percent reduction of overall bottleneck discharge rate varies from
3 to 17%, and the immediate reduction from 3 to 22%. Based on the result in Table 7, the
variations in the percent reduction are attributable to variations in both pre-queue flow and
bottleneck discharge rate after the queue formations. In this section, we examine the variations in
pre-queue flow, the maximum flow sustained prior to traffic breakdown, and bottleneck
discharge rate during congestion.
Variations in pre-queue flow. The variations in pre-queue flow, the maximum flow
sustained prior to traffic breakdown, are analyzed with respect to merging and diverging flows.
The motivation for choosing these explanatory variables stems from the earlier findings that
lane-changes due to merging and weaving can instigate queue formations (Yeon et al., 2007;
Rudjanakanoknad and Akaravorakulchai, 2011) but that freeway-to-ramp maneuvers to exit the
freeway may have a different impact than ramp-to-freeway maneuvers (Rudjanakanoknad and
Akaravorakulchai, 2011). Indeed Figure 6 shows that the pre-queue flow is positively related to
70
the diverging flow (Figure 21(a)), whereas it is negatively related to the merging flow (Figure
21(b)). The latter relationship is not as clear, and a multiple regression analysis verifies that the
merging flow is not statistically significant at the 95% confidence level. This is attributable to (i)
the low resolution of the on-ramp data (5 minutes) and/or (ii) disproportionately large diverging
flow, which may have a dominant influence. Nevertheless, the result suggests that ramp-to-
freeway lane-changes may have a more disruptive effect in traffic flow than freeway-to-ramp
maneuvers. This finding is also consistent with the finding of Rudjanakanoknad and
Akaravorakulchai (2011).
71
(a)
(b) Figure 21. (a) Pre-queue flow vs. pre-queue off-ramp flow; (b) Pre-queue flow vs. pre-queue on-ramp flow.
Variations in bottleneck discharge rate. We now present the variations in bottleneck
discharge rate during congestion. Figure 22(a) shows the total flow across all lanes and the flow
in the HOV lane over 5-minute intervals on 10/28/2008. The figure shows that the flow reaches
its maximum around 14:40 and instigates the onset of queue. After the queue formation, the
bottleneck discharge rate diminishes significantly until the HOV lane becomes active at 15:00.
Thereafter, the bottleneck discharge rate partially recovers and remains generally higher than the
prior rate for about 1.5 hours. The figure further illustrates that this recovery in discharge rate is
attributable to the smoothing effect. Notably, the temporal trend of the HOV lane flow is nearly
10000
10500
11000
11500
12000
12500
2400 2600 2800 3000P
re-q
ueue
flo
w (
veh
/hr)
Pre-queue off-ramp flow (veh/hr)
10000
10500
11000
11500
12000
12500
1100 1300 1500 1700
Pre
-que
ue f
low
(ve
h/hr
)
Pre-queue on-ramp flow (veh/hr)
72
opposite to that of the discharge rate, indicating that fewer lane-changes toward the HOV lane
promote higher bottleneck discharge rates. The trend is contrary in the regular-use lanes; see
Figure 22(b). The regular-use lanes experience markedly higher utilization after the HOV lane
activation, presumably induced by restricted access to the HOV lane. (Note that because there is
additional capacity downstream of the diverge due to the split of lane 3 (see Figure 18), the
changes in lane flow represent the changes in lane utilization, rather than lane-wise bottleneck
discharge rates.)
(a)
Figure 22. Smoothing effects over time on 10/20/2008; (a) Temporal trends of total flow vs. flow in the HOV lane; (b) Temporal trends of total flow vs. flows in the regular-use lanes and exit lanes.
900
1000
1100
1200
1300
1400
1500
1600
9000
9500
10000
10500
11000
11500
12000
12500
14:30 14:45 15:00 15:15 15:30 15:45 16:00 16:15 16:30 16:45
Flow
in H
OV
lane
(ve
h/hr
)
Tota
l flo
w (
veh/
hr)
Total flow
HOV lane
Queueonset
HOV lane
“Capacity drop”
73
(b)
Figure 22(contd.). Smoothing effects over time on 10/20/2008; (a) Temporal trends of total flow vs. flow in the HOV lane; (b) Temporal trends of total flow vs. flows in the regular-use lanes and exit lanes.
We further investigate the causality between HOV LFD and bottleneck discharge rate at
the time of bottleneck activation and HOV lane activation. A cross-correlation analysis revealed
that at the time of bottleneck activation, an increase in HOV LFD preceded a reduction in
discharge rate (i.e., immediate capacity drop) on nearly 70% of the study days (23 of 33 days).
The average lag time was around 3 minutes. Conversely, a reduction in HOV LFD preceded an
increase in the discharge rate at the time of HOV lane activation. This trend was observed on 75
% of the study days (25 of 33 days) with the average lag time of 3.6 minutes.
3000
3500
4000
4500
5000
5500
6000
9000
9500
10000
10500
11000
11500
12000
12500
14:30 14:45 15:00 15:15 15:30 15:45 16:00 16:15 16:30 16:45
Flow
s in
reg
ular
-use
and
exi
t lan
es (
veh/
hr)
Tota
l flo
w (
veh/
hr)
Total Flow
Regular Lanes
Exit lanes
Queueonset
HOV lane
“Capacity drop”
74
Table 9 provides the basic statistics of the result. The bottleneck discharge rate increases
from 10,299 to 10,714 veh/hr on average in the presence of smoothing effect, and this 4%
increase is statistically significant. Moreover, judging by the ranges, the discharge rate is as large
as 12,943 veh/hr, exceeding the pre-queue flow by more than 18%. Indeed on several days, the
discharge rate in the presence of smoothing effect exceeded the pre-queue flow. The smoothing
effect persisted for approximately 1.5 hours on average.
Table 9.
Summary statistics of the smoothing effect magnitude and duration.
Summary statistics Average (Standard Error)
Range
Bottleneck discharge rate before HOV lane activation (veh/hr)1
10,299 (39.5) 9,447 to 10,942
Bottleneck discharge rate with smoothing effect (veh/hr)
10,714 (13.74) 10,714 to 12,943
Duration of smoothing effect (minutes) 92.5 (9.8) 24 to 181 1 average discharge rate after the immediate capacity drop and before HOV lane activation
Notice in Figure 22(a) that the HOV lane flow gradually recovers after about 1 hour and
15 minutes. However, the trend of the bottleneck discharge rate is contrary; it gradually
diminishes over time, implying waning smoothing effect. Clearly, lower utilization of the HOV
lane promotes higher bottleneck discharge rates. The highest HOV LFD in the presence of the
smoothing effect was 0.288 (standard error = 0.002) on average across study days.
From the Figure 22(a) and 22(b), it is evident that there exists oscillations, where the total
flow increases and decreases alternatively. Table 10 provides the day to day variations in the
period of these oscillations. It was the found that the average period of oscillation is 32 minutes.
The reason for these oscillations should be further investigated and is not in the scope of this
research.
75
Table 10.
Total flow-oscillations statistics.
To gain further insight, Figure 8 presents LFD vs. the bottleneck discharge rate while the
HOV lane was active; the data points come from all study days. The LFDs are computed based
on the near-steady state flows that are identified via CWT. The trends are approximately linear,
as observed by several previous studies (e.g., Duret et al., 2012). More importantly, the
bottleneck discharge rate improves as the HOV and exit LFDs decrease. This observation is
DayAvg. Cycle
Duration (mins)Variation Cycle Duration (mins)
6/3/2008 33.05 6.95
6/4/2008 27.09 8.62
6/6/2008 35.71 13.03
6/11/2008 43.16 25.84
7/11/2008 29.17 2.73
7/30/2008 41.44 10.22
8/6/2008 31.23 7.24
8/8/2008 29.33 5.47
8/13/2008 30.1 4.9
9/3/2008 35.44 11.6
9/15/2008 44.42 18.88
9/16/2008 38.19 8.8
9/19/2008 30.19 5.3
10/6/2008 29.66 4.65
10/8/2008 41.47 10.88
10/9/2008 27.07 5.56
10/20/2008 28.18 5.03
11/3/2008 36.29 14.23
11/4/2008 29.38 7
11/10/2008 26.15 7.28
11/20/2008 39.2 11.63
11/24/2008 31.33 5
12/3/2008 30.99 2.71
12/15/2008 26.71 10.91
12/17/2008 39.38 27.82
1/5/2009 27.16 3.66
1/7/2009 29.58 19.12
1/13/2009 26.56 6.32
1/23/2009 43.14 11.59
76
further confirmed with a regression analysis; see Table 3 for the result. Notice that the effect of
the HOV LFD (and thus the smoothing effect) is more significant than that of the exit LFD. One
would expect fewer leftward lane changes with diminishing HOV LFD and similarly, fewer
rightward (freeway-to-ramp) lane changes with the diminishing exit LFD.
Table 6.
A summary of regression result: bottleneck discharge rate vs. exit LFD and HOV LFD.
Predictor Coefficient Standard error t-value p-value Constant 17,349.4 636.7 27.25 0.000 Exit LFD -8,944 1,107 -8.08 0.000 HOV LFD -13,530 1,127 -12.00 0.000
Analysis of variance
Source DF SS MS F P Regression 2 31,619,226 33,417,851 72.85 0.000 Residual Error 729 158,200,060 215,117 Total 731 189,819,286
S= 465.843, R2 = 0.167, Adjusted R2 = 0.164
Thus, the findings suggest that (i) higher bottleneck discharge rates are attained with
fewer lane changes and that (ii) the smoothing effect by restricting access to the HOV lane has a
more profound impact on the bottleneck discharge rate than diverging flow.
77
Figure 23. LFDs vs. bottleneck discharge rate after HOV lane activation. Conclusions
This study analyzed the characteristics of a freeway weave bottleneck with a HOV lane.
On each of 33 study days, a queue formed consistently, well before the activation of the HOV
lane, upon simultaneous surges in on-ramp and off-ramp flows. Thereafter the bottleneck
discharge rate diminished by 3-22% in the presence of queue. The discharge rate, however,
recovered substantially with HOV lane activation presumably due to the smoothing effect
induced by fewer disruptive lane-changes toward the HOV lane. The discharge rate improved by
approximately 4% on average and occasionally exceeded the maximum flow prior to the queue
formation. The smoothing effect persisted for 1.5 hours on average, though it waned over time as
the HOV lane gradually became more utilized.
0.7 0.8 0.9 1 1.1 1.2 1.3
x 104
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Total flow (veh/hr)
Lane
flo
w d
istr
ibut
ion
Lane 3 Lane 2 Lane 1 HOV Lane EXIT Lane
78
This study further examined the variations in bottleneck discharge rate. The HOV LFD
and the proportion of flow diverging were found to be significant variables that negatively affect
the bottleneck discharge rate. Of the two variables, the HOV LFD, a surrogate measure of the
smoothing effect, had a more significant impact on the discharge rate. This finding underscores
the significance of the smoothing effect, particularly in light of the fact that the diverging flow
constituted a large fraction of flow (≈ 23%) in this study.
The smoothing effect has been conjectured by Menendez and Daganzo (2007) and
empirically verified by Cassidy et al. (2010) at a merge and a curve bottlenecks. Our findings
corroborated that a HOV lane can also induce the smoothing effect at a weave bottleneck by
discouraging lane-changes toward the HOV lane. This effect, measured by the HOV LFD, was
evidently the dominant factor for the variations in bottleneck discharge rate. Our findings
provided further insight into the characteristics of the smoothing effect, including its magnitude
and temporal trend, in a statistically rigorous manner.
Nevertheless, some future studies are needed. Since bottleneck characteristics can be site-
specific, it is desirable to verify the reproducibility of the results on a more balanced weaving
bottleneck (in terms of merging and diverging flows). Moreover, the waning smoothing effect
over time was accompanied by increasing HOV LFD. The reason behind increasing HOV LFD
is not clear, although it may be demand driven. Finally, our results suggest that one can sustain
high bottleneck discharge rate by limiting the HOV LFD. A more in-depth study would be
useful, especially from the control standpoint, to determine the optimal level of HOV LFD that
maximizes the bottleneck discharge rate.
79
CHAPTER 6
LANE FLOW DISTRIBUTION AND ITS RELATIONSHIP WITH BOTTLENECK
DISCHARGE RATE
This chapter explores the relationship between lane flow distribution and bottleneck
discharge rate at weaving bottleneck occurred due to a lane drop and a busy off-ramp. Previous
studies explored the relationship of speed and flow across different lanes with the total flow on
the freeway segments. They observed that high flows before the bottleneck activation were
associated with vehicle lane changes towards the median lane and observed reduction in flows in
all the lanes after the bottleneck activation. However, not much work has been done on studying
the relationship of lane flow distributions at weaving bottleneck locations occurred due to a lane
drop and a busy off-ramp.
We believe that this study is an important contribution given that the previous studies
analyzed weaving bottlenecks that occurred due to busy on-ramp and busy off-ramps. The
bottleneck studied in this case is a weaving bottleneck that occurred due to a lane drop and a
busy off-ramp. Also the fact that these kind of weaving bottlenecks are quite common and not
been studied before adds to the significance of this study. The studies on weaving bottlenecks
resulted from a busy merge and diverge flows showed that ramp-to-freeway maneuvers are
disruptive in nature. However in this case, a different pattern has been observed given that the
weave geometry of this study is different from earlier studies . This Chapter focuses on
establishing the relationship of lane flow distribution with variation of bottleneck discharge rate
on a bottleneck site located on US-101south in the Los Angeles County in California. The results
confirmed that both the pre-queue flow and discharge rate are linearly related with LFD. It was
found that more the lane changing towards the median lane, the more is the lane utilization of the
80
median lane and more is the discharge rate. The lane changes towards the off-ramp from the
median lane would be disruptive and would result in lower discharge rate.
Site and data
The selected study site is a southbound section of US route 101, located between Barham
Blvd. and Lankershim Blvd. in the Los Angeles County in California. The bottleneck schematic
is shown in Figure 24(a). The site contains five regular use lanes which get tapered into four
regular use lanes and an off-ramp near the bottleneck location. The shoulder lane (lane 5)
becomes an exit only lane just downstream of post mile (PM) 10.2 whereas lane 4 has the option
of exiting to the off-ramp. There is no HOV lane at this location. A recurrent bottleneck resides
between PM 10.2 and PM 9.9 presumably due to the major diverge in this freeway section and
lane reduction at the diverge. A typical speed contour shown in Figure 24(b) further confirms the
location of the bottleneck. The length of the queue was found to be greater than 3 miles.
Eighteen days of data during the months spanning from October 2013 to January 2014
were used for this analysis when the study section was free of reported incidents and was an
active bottleneck. 5-minute data has been used for the preliminary analysis and 30-second data
de-noised using discrete wavelet transforms was used for detailed analysis of the bottleneck. The
data are obtained from the California freeway performance measurement system (PeMS)
database. Data are available from all the detector locations as labeled in Figure 24(a) and consist
of vehicle count, occupancy and time-mean speed aggregated over 5minute and 30-second
intervals.
81
(a)
(b) Figure 24. Bottleneck location on US-101 southbound (a) Schematic (b) Speed contour on 01-31-14. Bottleneck activation and congestion pattern
For this analysis, the wavelet transform (WT) is used to de-noise the 30-second raw data,
precisely identify bottleneck activation and deactivation times, and measure pre-queue flow and
discharge rate. The procedure for the application of wavelet transforms is described in detail in
Chapter 3. It was observed that the bottleneck activated around 17:22 in the evening with an
average duration of 2 hrs and 3 minutes. The average pre-queue flow (maximum flow sustained
prior to the bottleneck activation as described in Chapter 3) was found to be 7,726 vph and the
Lane 1Lane 2Lane 3Lane 4Lane 5
PM 9.9PM 10.2PM 10.7PM 11.2PM 11.4PM 11.9PM 12.5
Barham Blvd.Lankershim Blvd.Ventura Blvd.Vineland Ave.
Approximate Bottleneck Location
EXIT ONLY
82
average discharge rate during congestion was found to be 7,037 vph, resulting in an average
overall capacity drop of 8.9%. The average off-ramp flow prior to the bottleneck activation when
the pre-queue was measured was 1,718 vph whereas the average off-ramp flow during
congestion was found to be 1,565 vph. Given that there is high diverge flow through the off-
ramp and a lane reduction, the resultant bottleneck is most likely a weave bottleneck. The results
are tabulated in the Table 12.
Table 12.
Bottleneck statistics.
Average (standard error)
No. of days 18
Time of onset of queue 17:22 (5.6 minutes)
Time of clearance of queue 19:25 (4.4 minutes)
Pre-queue flow (veh/hr) 7,726 (62)
Bottleneck discharge rate (veh/hr) 7,037 (82)
Reduction in bottleneck discharge rate (veh/hr) 688 (73) Reduction in bottleneck discharge rate (%) 8.88 (1)
The speed profile at the detector immediately upstream of the bottleneck on a study day
is shown in Figure 25. The times of congestion activation and deactivation were identified using
continuous wavelet transforms. The figure shows that lane 4 is the most congested among the
lanes whereas lane 1 (median lane) is the least congested. Congestion starts in the lanes
associated with the exit lanes, where intense weaving activities likely occur and spreads to the
inside lanes. Figure 26 shows the relationship between flow and speed for each lane at the
detector immediately upstream of the bottleneck on all days. The figure illustrates that during
free flow conditions, the speed is relatively constant. For lanes 3-5, data points during congested
periods lie well below those during free-flow periods, and a decrease in speed is associated with
the reduction in flow. Interestingly, for lanes 1 and 2, data points during “congested periods” lie
83
between the free-flow branch and the congested branch (based on lanes 3-5). Moreover, speed is
rather insensitive to the flow. These patterns suggest that flows in lanes 1 and 2 are not restricted,
and the speeds lower than free-flow speed may be attributable to the low congested speeds in the
adjacent lanes; i.e., drivers may choose to travel at lower speeds in response to conditions in the
adjacent lanes.
Figure 25. Speed profile of the upstream detector on 01/10/2014.
20
30
40
50
60
70
80
90
14:00:00 14:30:00 15:00:00 15:30:00 16:00:00 16:30:00 17:00:00 17:30:00 18:00:00 18:30:00 19:00:00 19:30:00 20:00:00 20:30:00
Sp
eeed
(m
ph
)
Time
Lane1 Lane 2 Lane 3 Lane 4 Lane 5
16:46:30
16:47:30
16:52:30
16:52:3016:58:30
19:32:30
19:33:00
19:29:00
19:33:00
19:33:00
84
Figure 26. Flow vs. speed at the upstream detector.
0
10
20
30
40
50
60
70
80
90
100
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
Spe
ed (
mp
h)
Flow (vph)
Lane 1
(a)
Free flow branch
0
10
20
30
40
50
60
70
80
90
100
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
Sp
eed
(m
ph)
Flow (vph)
Lane 2
(b)
Free flow branch
85
Figure 26 (contd.). Flow vs. speed at the upstream detector.
0
10
20
30
40
50
60
70
80
90
100
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
Sp
eed
(m
ph)
Flow (vph)
Lane 3
(c)
Free flow branch
0
10
20
30
40
50
60
70
80
90
100
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
Spee
d (
mph
)
Flow (vph)
Lane 4
(d)
Free flow branch
86
Figure 26 (contd.). Flow vs. speed at the upstream detector.
Lane flow distribution (LFD) and its effect on discharge rate
Figure 27 shows the LFD of the four lanes on a typical day at the detector located at
milepost 9.9, immediately downstream of the bottleneck. The bottleneck activation and de-
activation times on this day were 5:15 p.m. and 7:50 p.m., respectively. Figure 27(a) shows that
the flow (demand) steadily increased from 3 pm until the bottleneck activated, and then a
reduction in discharge rate is observed during congestion. The increase in the flow before
congestion is accompanied by an increase in LFD in the median lane and a decrease in the LFD
of the shoulder lane as shown in Figure 27(b). There are no significant changes observed in the
LFDs of lanes 2 and 3. This shows that as the flow increases before congestion, there is an
increase in the utilization of the median lane indicating systematic lane changes towards the
median lane. However during congestion, opposite patterns were observed. The reduction in
discharge rate was accompanied by a reduction in LFD in the median lane and an increase in
LFD in the shoulder lane. The LFD in the median lane at the time of bottleneck activation varied
0
10
20
30
40
50
60
70
80
90
100
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
Spe
ed (
mp
h)
Flow (vph)
Lane 5
Free flow branch
(e)
87
from 0.20 to 0.26 across the study the days. The LFD in the shoulder lane varied from 0.22 to
0.27 at the time of bottleneck activation.
Figure 27. LFD vs. discharge rate on 01/31/14 at detector located milepost 9.9.
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
12:00:00 PM 3:00:00 PM 6:00:00 PM 9:00:00 PM 12:00:00 AM
Flow (vph)
Flow (vph)
0.1
0.15
0.2
0.25
0.3
12:00:00 PM 3:00:00 PM 6:00:00 PM 9:00:00 PM 12:00:00 AM
LFD
LFD lane 1 LFD lane 4
0.1
0.15
0.2
0.25
0.3
12:00:00 PM 3:00:00 PM 6:00:00 PM 9:00:00 PM 12:00:00 AM
LFD
LFD lane 2 LFD lane 3
BN activation time
BN de ‐activation time
(a)
(b)
(c)
88
To better understand the causality between the change in LFD in the median lane and the
change in discharge rate at the bottleneck activation, a cross-correlation analysis has been
conducted using 30 second data. Figure 28 shows the cross-correlation at different time lags
between the discharge rate and LFD in the median lane on 01/31/14. Each time lag represents a
time step of 30-seconds. A positive time lag means that the flow is a leading variable to the
HOV LFD where as a negative lag indicated that HOV LFD is the leading variable. The figure
shows that the discharge rate is positively correlated to the LFD in the median lane, confirming
the observation above (Figure 27). Also it can be seen that the maximum correlation is observed
with a negative lag of 3. This result indicates that the change in the LFD in the median
preceded the change in discharge rate which implies that higher the utilization of the median lane
the higher is the discharge rate. The lag of 3 indicates that the time lag between LFD in the
median lane and flow is 1.5 minutes. The cross correlation factor was statistically significant at
95% confidence interval.
Figure 28. Cross-correlation between the flow and LFD in the median lane (01/31/14).
0.785
0.79
0.795
0.8
0.805
0.81
0.815
0.82
0.825
0.83
0.835
-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Cro
ss C
orre
lati
on F
unc
tion
Val
ue
Time lag (each time lag is 30 secs)
89
Relationship between discharge rate and LFD during pre-congestion. Figure 29
shows the relationship between the LFD and the pre-queue just before the activation of the
bottleneck for the 18 study days. LFD of the median lane is positively related with the pre-queue
flow and this relationship is significant at 90% confidence level. LFD of the shoulder lane is
negatively related to the pre-queue flow and this relationship is significant at 95% confidence
level. Lanes 2 and 3 have a similar relationship with the pre-queue flow as lanes 1 and lane 4
respectively even though these relationships are not statistically not significant. These results
show that the more the median lane is utilized just before the bottleneck activation the higher is
the pre-queue flow. As seen earlier in this chapter the congestion is observed in the right most
lanes and then progressively proceeds towards the median lanes. Hence the vehicles tried to
move away from the right lanes towards the less congested/high speed lanes and thus resulting in
higher pre-queue flow.
(a)
Figure 29. LFD vs. Pre-queue flow, (a) Lane 1 (b) Lane 2 (c) Lane 3 (d) Lane 4.
y = 6768.7x + 6109.7R² = 0.172
7300
7400
7500
7600
7700
7800
7900
8000
8100
8200
0.15 0.17 0.19 0.21 0.23 0.25 0.27
Pre
-que
ue
flow
(vp
h)
LFD
Lane 1
90
(b)
(c)
(d)
Figure 29(contd.). LFD vs. Pre-queue flow, (a) Lane 1 (b) Lane 2 (c) Lane 3 (d) Lane 4.
y = 4269.7x + 6561.8R² = 0.0409
7300
7400
7500
7600
7700
7800
7900
8000
8100
8200
0.15 0.2 0.25 0.3
Pre
-qu
eue
flow
(vp
h)
LFD
Lane 2
y = -10194x + 10281R² = 0.0894
7300
7400
7500
7600
7700
7800
7900
8000
8100
8200
0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29
Pre
-que
ue
flow
(vp
h)
LFD
Lane 3
y = -8814.8x + 9877.6R² = 0.231
7300
7400
7500
7600
7700
7800
7900
8000
8100
8200
0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29
Pre
-que
ue
flow
(vp
h)
LFD
Lane 4
91
Relationship between discharge rate and LFD during congestion. Figure 30 shows
the relationship between LFD and the discharge rate after the activation of the bottleneck for the
18 study days. LFD of the median lane decreases along with the discharge rate after the onset of
congestion whereas LFDs of lane 3 and lane 4 increase with the reduction in the discharge rate.
Lane 2 LFD does not change significantly during this period. The linear relationships between
the discharge rate and LFDs of lane 1, lane 3 and lane 4 were found to be statistically significant
at the 95% confidence level. The results show that the more the median lane is utilized during the
congestion, the higher is the discharge rate (recall that flows in lanes 1 and 2 were found to be
unrestricted). It could be seen that higher the lane utilization of left lanes (lane 1 and lane 2) the
higher are the lane changes away from the right lanes (lane 3 and lane 4) and higher is the
discharge rate. The linear relationships between the discharge rate and difference in LFDs of lane
1, lane 2 with lane 4 were found to be statistically significant at the 95% confidence level.A
more detailed analysis will follow.
(a)
Figure 30. LFD vs. discharge rate, during congestion (a) Lane 1 (b) Lane 2 (c) Lane 3 (d) Lane 4.
y = 23165x + 1653.4R² = 0.2919
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 0.05 0.1 0.15 0.2 0.25 0.3
Dis
char
ge r
ate
(vph
)
LFD
Lane 1
92
(b)
(c)
(d)
Figure 30(contd.). LFD vs. discharge rate, during congestion (a) Lane 1 (b) Lane 2 (c) Lane 3 (d) Lane 4.
y = 6744.8x + 5037.7R² = 0.0107
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.1 0.15 0.2 0.25 0.3 0.35
Dis
char
ge r
ate
(vph
)
LFD
Lane 2
y = -14897x + 10642R² = 0.0571
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.1 0.15 0.2 0.25 0.3 0.35
Dis
char
ge r
ate
(vph
)
LFD
Lane 3
y = -26047x + 13434R² = 0.2698
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.1 0.15 0.2 0.25 0.3 0.35
Dis
char
ge r
ate
(vph
)
LFD
Lane 4
93
Figure 31 shows the relationship between the difference in magnitudes of the LFDs
between the lanes and discharge rate. These results indicate that the higher the lane utilization of
the median and lane 3 (left lanes) the higher is the discharge rate.
(a)
(b)
Figure 31. Difference in magnitudes between lane LFDs vs. discharge rate, during congestion.
To gain more evidence on lane changing, both speed and flow data from the detector
located just upstream of the bottleneck were analyzed. The amount of systematic (net) lane
changing around the bottleneck was measured by taking the difference in flow between the
y = -15578x + 7294.7R² = 0.3576
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
-0.1 -0.05 0 0.05 0.1 0.15
Dis
char
ge r
ate
(vph
)
LFD
LFD Lane 4 - LFD Lane 1
y = -14023x + 6634.6R² = 0.1675
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
Dis
char
ge r
ate
(vph
)
LFD
LFD Lane 4 - LFD Lane 2
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upstream and downstream of the bottleneck. Figure 32 shows the relationship between the net
lane-changing in individual lanes and the discharge rate. From the figure, it is evident that (i)
there are systematic lane changes away from lane 1 judging by negative changes in flow and that
(ii) the more the lane changes away from the median lane, the lower is the discharge rate. An
increase in lane changes toward lane 2 resulted in an increase in discharge rate. These results
indicate that there is a systematic lane changing towards lane 2 indicating merging activity due
to the lane reduction in addition to the large diverge flow. This supports that the bottleneck is a
weaving bottleneck. The relationships between the changes in flow in lane 3 and lane 4 and the
discharge rate were not statistically significant.
95
(a)
(b)
Figure 32. Relationship between difference in flow between downstream and upstream detector and discharge rate.
y = 0.0899x - 725.53R² = 0.3721
-250
-200
-150
-100
-50
0
5000 5500 6000 6500 7000 7500 8000
Ch
ange
in f
low
(vp
h)
Discharge rate (vph)
Change in flow: Lane 1
y = 0.1141x - 606.37R² = 0.5449
0
50
100
150
200
250
300
5000 5500 6000 6500 7000 7500 8000
Cha
nge
in f
low
(vp
h)
Discharge rate (vph)
Change in flow: Lane 2
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(c)
(d)
Figure 32 (contd.). Relationship between difference in flow between downstream and upstream detector and discharge rate.
These results indicate that a higher discharge rate is attained by fewer lane changes
toward the off-ramp that likely promote better utilization of the median lane. An increase in off
ramp flow results in an increase in lane changes away from the median lane reducing its lane
utility thereby reduction in discharge rate. This result is contradicting to an earlier study by Lee
y = 0.0019x - 57.515R² = 0.0004
-100
-80
-60
-40
-20
0
20
5000 5500 6000 6500 7000 7500 8000
Ch
ange
in f
low
(vp
h)
Discharge rate (vph)
Change in flow: Lane 3
y = -0.0199x + 106.46R² = 0.0067
-200
-150
-100
-50
0
50
100
150
200
5000 5500 6000 6500 7000 7500 8000
Cha
nge
in f
low
(vp
h)
Discharge rate (vph)
Change in flow: Lane 4
97
et al. (Lee and Cassidy, 2009) which stated that the lane changes towards the median lanes are
disruptive. The weaving bottlenecks previously analyzed in literature involved a busy on-ramp
and a busy off-ramp but in this case, the weaving activity is a result of combination of a lane
drop and a busy off-ramp. Another significant difference in the geometry in this case, that is, the
merge and diverge activities occur at the same location when compared to the other bottlenecks
analyzed where the merge (on-ramp) and diverge (off-ramp) activities occur at different
locations.
Conclusion
This chapter explored the relationship between lane flow distributions and bottleneck
discharge rate on weaving bottleneck involving a lane drop and a busy off-ramp. To this end, 18
study days where the queue has formed consistently due to a diverge/off-ramp and lane
reduction. The average reduction in bottleneck discharge rate upon bottleneck activation was
found to be around 9%.
The speed profile at the detector immediately upstream of the bottleneck showed that
lane 4 is the most congested among the lanes whereas lane 1(median lane) is the least congested.
Further it was found that the congestion occurs first in the rightmost lanes and spread
progressively towards the inner lanes. Also it was found that during congestion lane 3, lane 4 and
lane 5 have lower speeds and high flows whereas lane 1 is the least congested. It was observed
that Lane 2 during congestion is associated with relatively high speed and discharge rate
respectively indicating that during congestion the inner lanes are more utilized.
It was observed that the increase in flow well before congestion started was accompanied
by the increase in the LFD of the median lane and upon bottleneck activation it was found that
the LFD in the median decreased with the reduction in the bottleneck discharge rate. Cross
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correlation analysis confirmed that the bottleneck discharge rate and LFD in the median lane are
positively correlated and the change in LFD in the median lane occurred first followed by the
change in the discharge rate. LFD of the median lane is found to be positively related with the
pre-queue flow and LFD of the shoulder lane is negatively related to the pre-queue flow. Further,
it was found that the LFDs of all the lanes are linearly related to the discharge rate. The LFD in
the median lane is positively related to the discharge rate whereas the LFDs in the shoulder lane
and lane 3 are negatively related. The relationship is found to be statistically significant in the
median lane, lane 3 and lane 4.
To gain more evidence on lane changing, both speed and flow data from the detector
located just upstream of the bottleneck were analyzed. It was found that more the lane changing
towards the median lane, the more is the lane utilization of the median lane and more is the
discharge rate. The lane changes towards the off-ramp from the median lane would be disruptive
and would result in lower discharge rate. We believe that this study is an important contribution
given the fact that the previous studies analyzed weaving bottlenecks that occurred due to busy
on-ramp and busy off-ramps. The bottleneck studied in this case is a weaving bottleneck that
occurred due to a lane drop and a busy off-ramp. From the results, it was found that the effect of
lane changing patterns in this case are quite opposite to those mentioned in the previous studies.
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CHAPTER 7
CONLUSIONS
Traffic congestion is a major externality in modern transportation systems and has a
negative economic, environmental, and social impact. One of the key elements that determine the
extent of congestion, besides the demand for travel by automobiles, is freeway bottlenecks. In
the previous studies, there has been a lack of efforts to systematically identify active bottlenecks
and measure the capacity drop on a regional network. Also most of the previous studies have
focused on studying the mechanisms of merge and diverge bottlenecks. Mechanisms and features
of weaving bottlenecks are not very well understood. Most of these studies have analyzed only a
few days of data and have not considered in identifying steady state periods in systematic and
reproducible manner.
This research developed an efficient methodology to identify and analyze freeway
bottlenecks in a region in a consistent and reproducible manner. To this end, using the regional
analysis methodology, 23 bottlenecks have been identified, some of which result in long queues
and large delays during rush-hour periods in the Phoenix metropolitan region. For these
bottlenecks, a number of performance measures were obtained, such as the duration of
congestion, length of the congestion, vehicle miles traveled (VMT), vehicles hours traveled
(VHT), and bottleneck discharge rate (where it can be measured or estimated). The identified
bottlenecks were ranked according to the capacity drop in terms of flow and percent reduction in
flow. This research showed that the 5-minute data could be effectively used in identifying and
prioritizing active bottlenecks in a region. However, for studying the detailed mechanism of the
high ranked active bottlenecks identified through the regional analysis it is advisable to use
higher resolution data with an effective de-noising methodology as many traffic phenomena like
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lane changing, traffic stationary periods, oscillations etc. occur at a frequency less than 5
minutes.
This research also investigated the features of two types of weaving bottlenecks in a
statistically rigorous manner. It examined the effect of HOV lane on the bottleneck discharge
rate and studied the factors that lead to the variation in bottleneck discharge rate. Data ranging
from 18 to 33 days has been used in this research and wavelet transforms were used to
effectively de-noise the data and identify key bottleneck events like congestion activation/de-
activation times and steady state periods in a systematic and reproducible manner. A
methodology has been developed to de-noise raw data using Discrete Wavelet Transforms
(DWT) and the de-noised data is then used to precisely identify key bottleneck events using
Continuous Wavelet Transforms (CWT).
This study specifically analyzed the characteristics of a freeway weave bottleneck with a
HOV lane. Results showed that the bottleneck discharge rate diminished by 3-22% upon queue
formations and recovered upon the high-occupancy-vehicle (HOV) lane activation, confirming
the existence of the “smoothing effect.” The recovery was substantial; the discharge rate
improved by 4% and occasionally exceeded the maximum pre-queue flow. The smoothing effect
persisted for about 1.5 hours and waned thereafter as the relative utilization of the HOV lane
gradually recovered. A statistical analysis corroborates that the HOV lane flow distribution
significantly (and negatively) affects the bottleneck discharge rate, more so than the amount of
diverging flow. From this study we found that: (i) a higher (lower) flow can be sustained prior to
traffic breakdown with higher diverging (merging) flow, suggesting that ramp-to-freeway
maneuvers are more disruptive; (ii) higher bottleneck discharge rates are attained with higher
diverging flow and activation of HOV lane.
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This research also explored the relationship between lane flow distribution and
bottleneck discharge rate at weaving bottleneck occurred due to a lane drop and a busy off-ramp.
There has not been work done in the past on studying the mechanism of a weave bottleneck that
occurred due to lane drop and a busy off-ramp and the results showed that the traffic patterns
observed in this type of weave bottleneck are different from those mentioned in the previous
studies. Data from 18 study days showed that the discharge rate diminished upon bottleneck
activation and the average reduction in bottleneck discharge was found to be around 9%. It was
found that the congestion occurred first in the rightmost lanes and spread progressively towards
the inner lanes. LFD of the median lane is found to be positively linearly related with the pre-
queue flow and LFD of the shoulder lane is negatively linearly related to the pre-queue flow. It
was found that an increase in lane changing towards the median lane resulted in higher median
lane utilization and higher discharge rate. The lane changes towards the off-ramp from the
median lane would be disruptive and would result in lower discharge rate.
Practical implications: The regional analysis methodology employed in this research
would help in identifying and prioritizing the bottlenecks by ranking them based on the capacity
drop. This would aid the local governing body to focus on the bottlenecks that require immediate
attention. Also the identified bottlenecks were attributed to a variety of factors, such as merging
at busy on-ramps or freeway-to-freeway connectors, weaving due to busy merges followed by
busy diverges (especially near major freeway-to-freeway interchanges), and curves. Since the
cause of the bottlenecks was identified it would enable the local governing body to act
accordingly to improve the freeway efficiency.
This research conducted detailed analysis of bottleneck features on two different types of
weaving bottlenecks where there is a limited understanding of their features. The results showed
102
that HOV lane on a weaving bottleneck could be beneficial to the system performance. It was
found that the discharge rate improved upon the activation of HOV lane and HOV lane
utilization has a significant effect on discharge rate. The current highway capacity manual does
not specifically address the effect of HOV lane on weaving bottleneck capacity calculations and
volume adjustments were made considering the peak hour factor, heavy vehicle presence and
driver population only. The findings from this research suggest that HOV lane specific
adjustments on volume such as HOV lane utilization or factor representing the percent increase
in total volume upon HOV activation (in this study, the average increase in bottleneck discharge
rate was found to be 4%) could be included. However more weaving bottleneck sites should be
analyzed to have consensus on these factors. Also it was found that the ramp to freeway
maneuvers were disruptive in nature. Ramp metering (Cassidy and Rudjanakanoknad, 2005)
could limit these disruptive lane changes by restricting the surge in flows from the ramp to the
freeway.
Further, the effect of lane flow distribution on the bottleneck discharge rate was studied
on a weaving bottleneck that occurred due to a busy off-ramp and a lane drop. This study is an
important contribution given the fact that the previous studies analyzed weaving bottlenecks that
occurred only due to busy on-ramp and busy off-ramps and it was found that the effect of lane
changing patterns on discharge rate in this case are quite opposite to those mentioned in the
previous studies. This could be due to the fact that the length of the weaving segment is different
and relatively shorter than the weaving sections formed by an on-ramp and an off-ramp.
Future work: From the analysis of the weaving bottleneck with HOV lane it was found
that there exist oscillations where the total flow increases and decreases alternatively with an
average cycle length of oscillation is 32 minutes. It would be interesting to study the relationship
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between the oscillations with discharge rate as part of the future research. Due to data
limitations, detailed lane changing analysis and the effect of lane changing on the bottleneck
discharge rate could not be studied in this research. However it would be interesting to
investigate the lane changing patterns and their effects on the bottleneck discharge rate at these
weaving bottleneck locations. As seen in the literature, the bottleneck characteristics could be
site-specific and hence it is important to see if these results are reproducible at other weaving
bottleneck locations. Also it would be interesting to determine the optimal level of HOV LFD
that maximizes the bottleneck discharge rate.
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